CS534 Final Report

Predicting Patient Length of Stay and Cost per Day

1 Introduction

Predicting patient outcomes early in the admission process is an important part of hospital management [1,2]. Estimating a patient’s length of stay, for instance, assists in logistics such as allocation of hospital resources [2]. The ability to predict patient-specific healthcare costs helps us gain understanding of the situations that lead to high healthcare costs and can inform future decisions in preventative care, which has been shown to be one of the best ways to decrease healthcare cost [3].

For our final project we will be using the Statewide Planning and Research Cooperative System (SPARCS) Inpatient De-identified File dataset (originally provided the New York State Department of Health [4]) as it appears on Kaggle to predict length of stay (LOS) in days, a metric used to assess hospital efficiency and quality of care [2,5,6], and patient cost per day. The full dataset contains nearly 2.35 million de-identified observations and 37 features about hospital inpatient discharge data for 2015.

2 Set Up

2.1 Libraries

library(ggplot2)
library(ggiraph)
library(kableExtra)
library(lme4)
library(spaMM)
spaMM.options(nb_cores = future::availableCores() - 2)

2.2 Miscellaneous Functions

report_table <- function(x, w = NULL, h = "500px", ec = NULL, rownames = FALSE) {
    scroll_box(kable_paper(kable_styling(kbl(x, row.names = rownames), full_width = T, 
        position = "center", bootstrap_options = c("striped", "hover"), fixed_thead = T), 
        full_width = T), fixed_thead = T, height = h, width = w, extra_css = ec)
}

report_plot <- function(x) {
    girafe_options(girafe(code = print(x)), opts_sizing(rescale = TRUE), opts_tooltip(opacity = 0.9, 
        css = "background-color:gray;color:white;padding:2px;border-radius:2px;"), 
        opts_hover(css = "cursor:pointer;"))
}

3 Data Import

# Import the data
dat <- read.csv("input/Hospital_Inpatient_Discharges__SPARCS_De-Identified___2015.csv", 
    colClasses = c(rep("factor", 10), "character", rep("factor", 21), "numeric", 
        rep("factor", 2), rep("character", 2)), na.strings = c("NA", ""))

In addition to the columns found in the Kaggle dataset, we will also be using the New York State Department of Health’s “Health Facility General Information” dataset [7] in order to incorporate Facility Type and Ownership Type variables into our analysis by matching on Facility ID.

# read in facility id and description columns from facility information dataset
dat_hf <- read.csv("input/Health_Facility_General_Information.csv", colClasses = c("factor", 
    rep("NULL", 2), "factor", rep("NULL", 28), "factor", rep("NULL", 3)), skipNul = TRUE)

# remove duplicate rows
dat_hf <- dat_hf[!duplicated(dat_hf), ]

# rename columns
colnames(dat_hf) <- c("Facility.Id", "Facility.Type", "Ownership.Type")

# merge datasets by Facility Id
dat <- droplevels(merge(dat, dat_hf, by = "Facility.Id", all.x = TRUE, sort = FALSE))

report_table(head(dat, 50))

Facility.Id	Health.Service.Area	Hospital.County	Operating.Certificate.Number	Facility.Name	Age.Group	Zip.Code…3.digits	Gender	Race	Ethnicity	Length.of.Stay	Type.of.Admission	Patient.Disposition	Discharge.Year	CCS.Diagnosis.Code	CCS.Diagnosis.Description	CCS.Procedure.Code	CCS.Procedure.Description	APR.DRG.Code	APR.DRG.Description	APR.MDC.Code	APR.MDC.Description	APR.Severity.of.Illness.Code	APR.Severity.of.Illness.Description	APR.Risk.of.Mortality	APR.Medical.Surgical.Description	Payment.Typology.1	Payment.Typology.2	Payment.Typology.3	Attending.Provider.License.Number	Operating.Provider.License.Number	Other.Provider.License.Number	Birth.Weight	Abortion.Edit.Indicator	Emergency.Department.Indicator	Total.Charges	Total.Costs	Facility.Type	Ownership.Type
66	Western NY	Cattaraugus	0401001	Olean General Hospital	30 to 49	147	F	White	Not Span/Hispanic	5	Emergency	Home or Self Care	2015	127	Chronic obstructive pulmonary disease and bronchiectasis	0	NO PROC	140	Chronic obstructive pulmonary disease	4	Diseases and Disorders of the Respiratory System	3	Major	Moderate	Medical	Medicare	Medicaid	NA	197453	NA	NA	0	N	Y	$18309.20	$10309.98	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	70 or Older	147	M	White	Not Span/Hispanic	3	Emergency	Home w/ Home Health Services	2015	108	Congestive heart failure; nonhypertensive	58	HEMODIALYSIS	194	Heart failure	5	Diseases and Disorders of the Circulatory System	3	Major	Major	Medical	Medicare	NA	NA	40003993	193890	NA	0	N	Y	$12310.76	$6034.20	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	70 or Older	148	F	White	Not Span/Hispanic	9	Emergency	Home or Self Care	2015	2	Septicemia (except in labor)	222	BLOOD TRANSFUSION	720	Septicemia & disseminated infections	18	Infectious and Parasitic Diseases, Systemic or Unspecified Sites	4	Extreme	Major	Medical	Medicare	NA	NA	266409	266335	NA	0	N	Y	$48242.20	$20494.93	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	50 to 69	OOS	F	White	Not Span/Hispanic	2	Elective	Home or Self Care	2015	100	Acute myocardial infarction	47	DX CARDIAC CATHETERIZTN	190	Acute myocardial infarction	5	Diseases and Disorders of the Circulatory System	2	Moderate	Moderate	Medical	Medicaid	NA	NA	90271326	183914	NA	0	N	N	$12794.77	$7369.54	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	70 or Older	147	F	White	Not Span/Hispanic	4	Emergency	Home w/ Home Health Services	2015	100	Acute myocardial infarction	0	NO PROC	190	Acute myocardial infarction	5	Diseases and Disorders of the Circulatory System	2	Moderate	Moderate	Medical	Medicare	NA	NA	266141	NA	NA	0	N	Y	$10292.68	$4001.00	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	18 to 29	141	M	White	Not Span/Hispanic	7	Emergency	Short-term Hospital	2015	130	Pleurisy; pneumothorax; pulmonary collapse	39	INCISION OF PLEURA	143	Other respiratory diagnoses except signs, symptoms & minor diagnoses	4	Diseases and Disorders of the Respiratory System	1	Minor	Minor	Medical	Medicaid	NA	NA	271326	273279	NA	0	N	Y	$14177.09	$7711.28	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	50 to 69	141	M	White	Not Span/Hispanic	9	Emergency	Home w/ Home Health Services	2015	660	Alcohol-related disorders	231	OTHER THERAPEUTIC PRCS	280	Alcoholic liver disease	7	Diseases and Disorders of the Hepatobiliary System and Pancreas	3	Major	Major	Medical	Medicare	NA	NA	40003993	239912	NA	0	N	Y	$21448.73	$9511.37	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	0 to 17	147	F	White	Not Span/Hispanic	3	Newborn	Home or Self Care	2015	218	Liveborn	0	NO PROC	640	Neonate birthwt >2499g, normal newborn or neonate w other problem	15	Newborns and Other Neonates with Conditions Originating in the Perinatal Period	1	Minor	Minor	Medical	Medicaid	NA	NA	256322	NA	NA	3400	N	N	$2393.10	$1327.02	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	0 to 17	147	F	White	Not Span/Hispanic	4	Newborn	Home or Self Care	2015	218	Liveborn	0	NO PROC	640	Neonate birthwt >2499g, normal newborn or neonate w other problem	15	Newborns and Other Neonates with Conditions Originating in the Perinatal Period	2	Moderate	Minor	Medical	Medicaid	NA	NA	182357	NA	NA	2900	N	N	$4191.00	$2136.17	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	70 or Older	147	F	White	Not Span/Hispanic	4	Elective	Skilled Nursing Home	2015	204	Other non-traumatic joint disorders	152	ARTHROPLASTY KNEE	302	Knee joint replacement	8	Diseases and Disorders of the Musculoskeletal System and Conn Tissue	1	Minor	Minor	Surgical	Medicare	Private Health Insurance	NA	257934	257934	NA	0	N	N	$29514.01	$59253.25	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	0 to 17	147	F	White	Not Span/Hispanic	1	Newborn	Home or Self Care	2015	218	Liveborn	0	NO PROC	640	Neonate birthwt >2499g, normal newborn or neonate w other problem	15	Newborns and Other Neonates with Conditions Originating in the Perinatal Period	1	Minor	Minor	Medical	Medicaid	NA	NA	231077	NA	NA	2700	N	N	$813.50	$459.49	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	50 to 69	140	M	White	Not Span/Hispanic	4	Emergency	Home or Self Care	2015	2	Septicemia (except in labor)	0	NO PROC	720	Septicemia & disseminated infections	18	Infectious and Parasitic Diseases, Systemic or Unspecified Sites	3	Major	Major	Medical	Medicare	Blue Cross/Blue Shield	NA	271326	NA	NA	0	N	Y	$10114.85	$4943.62	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	0 to 17	147	M	White	Not Span/Hispanic	2	Newborn	Home or Self Care	2015	218	Liveborn	115	CIRCUMCISION	640	Neonate birthwt >2499g, normal newborn or neonate w other problem	15	Newborns and Other Neonates with Conditions Originating in the Perinatal Period	1	Minor	Minor	Medical	Medicaid	NA	NA	231077	231077	NA	2600	N	N	$1510.00	$929.25	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	50 to 69	147	M	White	Not Span/Hispanic	2	Emergency	Home or Self Care	2015	129	Aspiration pneumonitis; food/vomitus	0	NO PROC	137	Major respiratory infections & inflammations	4	Diseases and Disorders of the Respiratory System	3	Major	Moderate	Medical	Medicaid	NA	NA	266141	NA	NA	0	N	Y	$7330.35	$2502.54	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	0 to 17	147	F	White	Not Span/Hispanic	2	Newborn	Home or Self Care	2015	218	Liveborn	0	NO PROC	640	Neonate birthwt >2499g, normal newborn or neonate w other problem	15	Newborns and Other Neonates with Conditions Originating in the Perinatal Period	2	Moderate	Minor	Medical	Medicaid	NA	NA	237701	NA	NA	2900	N	N	$1528.50	$907.69	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	0 to 17	148	M	White	Not Span/Hispanic	1	Newborn	Home or Self Care	2015	218	Liveborn	115	CIRCUMCISION	640	Neonate birthwt >2499g, normal newborn or neonate w other problem	15	Newborns and Other Neonates with Conditions Originating in the Perinatal Period	1	Minor	Minor	Medical	Medicaid	Medicaid	NA	237701	60001091	NA	3200	N	N	$851.50	$496.77	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	18 to 29	147	F	White	Not Span/Hispanic	3	Elective	Home or Self Care	2015	187	Malposition; malpresentation	134	CESAREAN SECTION	540	Cesarean delivery	14	Pregnancy, Childbirth and the Puerperium	1	Minor	Minor	Surgical	Medicaid	NA	NA	147483	147483	NA	0	N	N	$8550.41	$4645.93	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	70 or Older	147	F	White	Not Span/Hispanic	10	Emergency	Inpatient Rehabilitation Facility	2015	51	Other endocrine disorders	0	NO PROC	424	Other endocrine disorders	10	Endocrine, Nutritional and Metabolic Diseases and Disorders	3	Major	Major	Medical	Medicare	NA	NA	40003993	NA	NA	0	N	Y	$17076.26	$9286.99	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	50 to 69	147	F	White	Not Span/Hispanic	13	Emergency	Skilled Nursing Home	2015	2	Septicemia (except in labor)	54	OT VASC CATH; NOT HEART	720	Septicemia & disseminated infections	18	Infectious and Parasitic Diseases, Systemic or Unspecified Sites	4	Extreme	Extreme	Medical	Medicare	Private Health Insurance	NA	197563	258490	NA	0	N	Y	$58394.67	$40505.88	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	70 or Older	OOS	F	White	Not Span/Hispanic	7	Emergency	Home w/ Home Health Services	2015	127	Chronic obstructive pulmonary disease and bronchiectasis	0	NO PROC	140	Chronic obstructive pulmonary disease	4	Diseases and Disorders of the Respiratory System	2	Moderate	Moderate	Medical	Medicare	Federal/State/Local/VA	NA	271326	NA	NA	0	N	Y	$17623.18	$8901.52	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	50 to 69	147	M	White	Not Span/Hispanic	2	Emergency	Home or Self Care	2015	103	Pulmonary heart disease	0	NO PROC	134	Pulmonary embolism	4	Diseases and Disorders of the Respiratory System	1	Minor	Minor	Medical	Medicaid	NA	NA	271326	NA	NA	0	N	Y	$8016.13	$2608.73	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	30 to 49	147	F	White	Not Span/Hispanic	7	Emergency	Home or Self Care	2015	657	Mood disorders	0	NO PROC	753	Bipolar disorders	19	Mental Diseases and Disorders	2	Moderate	Minor	Medical	Medicaid	NA	NA	40003856	NA	NA	0	N	Y	$7380.68	$9880.01	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	0 to 17	147	M	White	Not Span/Hispanic	3	Newborn	Home or Self Care	2015	218	Liveborn	115	CIRCUMCISION	640	Neonate birthwt >2499g, normal newborn or neonate w other problem	15	Newborns and Other Neonates with Conditions Originating in the Perinatal Period	1	Minor	Minor	Medical	Blue Cross/Blue Shield	NA	NA	182357	182357	NA	3200	N	N	$1964.00	$1261.62	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	50 to 69	147	M	White	Not Span/Hispanic	4	Emergency	Home w/ Home Health Services	2015	11	Cancer of head and neck	71	GASTROSTOMY; TEMP/PERM	110	Ear, nose, mouth, throat, cranial/facial malignancies	3	Ear, Nose, Mouth, Throat and Craniofacial Diseases and Disorders	3	Major	Moderate	Medical	Private Health Insurance	Federal/State/Local/VA	NA	256322	251671	NA	0	N	Y	$7568.00	$5248.66	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	70 or Older	148	M	White	Not Span/Hispanic	6	Emergency	Skilled Nursing Home	2015	50	Diabetes mellitus with complications	0	NO PROC	468	Other kidney & urinary tract diagnoses, signs & symptoms	11	Diseases and Disorders of the Kidney and Urinary Tract	3	Major	Major	Medical	Medicare	Private Health Insurance	NA	276511	NA	NA	0	N	Y	$10902.98	$5216.32	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	50 to 69	147	F	White	Not Span/Hispanic	4	Emergency	Home or Self Care	2015	127	Chronic obstructive pulmonary disease and bronchiectasis	216	RESP INTUB/MECH VENTIL	140	Chronic obstructive pulmonary disease	4	Diseases and Disorders of the Respiratory System	3	Major	Extreme	Medical	Medicare	NA	NA	165169	273279	NA	0	N	Y	$14544.13	$6380.94	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	0 to 17	141	F	White	Not Span/Hispanic	2	Newborn	Home or Self Care	2015	218	Liveborn	0	NO PROC	640	Neonate birthwt >2499g, normal newborn or neonate w other problem	15	Newborns and Other Neonates with Conditions Originating in the Perinatal Period	1	Minor	Minor	Medical	Blue Cross/Blue Shield	NA	NA	182357	NA	NA	2500	N	N	$1216.42	$811.52	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	30 to 49	148	F	White	Not Span/Hispanic	2	Emergency	Home or Self Care	2015	657	Mood disorders	0	NO PROC	753	Bipolar disorders	19	Mental Diseases and Disorders	1	Minor	Minor	Medical	Federal/State/Local/VA	NA	NA	267162	NA	NA	0	N	Y	$2415.05	$1876.09	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	30 to 49	147	F	White	Not Span/Hispanic	1	Elective	Home or Self Care	2015	196	Other pregnancy and delivery including normal	137	OT PRCS TO ASSIST DELIV	541	Vaginal delivery w sterilization &/or D&C	14	Pregnancy, Childbirth and the Puerperium	1	Minor	Minor	Surgical	Federal/State/Local/VA	NA	NA	197563	197563	NA	0	N	N	$4256.44	$3224.37	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	18 to 29	147	M	White	Not Span/Hispanic	5	Emergency	Home or Self Care	2015	657	Mood disorders	0	NO PROC	751	Major depressive disorders & other/unspecified psychoses	19	Mental Diseases and Disorders	1	Minor	Minor	Medical	Blue Cross/Blue Shield	Medicaid	NA	267162	NA	NA	0	N	Y	$5176.78	$6235.63	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	50 to 69	147	F	White	Not Span/Hispanic	9	Emergency	Skilled Nursing Home	2015	42	Secondary malignancies	231	OTHER THERAPEUTIC PRCS	952	Nonextensive procedure unrelated to principal diagnosis	4	Diseases and Disorders of the Respiratory System	3	Major	Major	Surgical	Medicare	Medicaid	NA	271326	239912	NA	0	N	Y	$22783.03	$12623.80	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	50 to 69	147	F	White	Not Span/Hispanic	2	Emergency	Home w/ Home Health Services	2015	127	Chronic obstructive pulmonary disease and bronchiectasis	0	NO PROC	140	Chronic obstructive pulmonary disease	4	Diseases and Disorders of the Respiratory System	2	Moderate	Moderate	Medical	Medicare	NA	NA	271326	NA	NA	0	N	Y	$15927.38	$5406.24	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	70 or Older	147	M	White	Not Span/Hispanic	3	Emergency	Home or Self Care	2015	62	Coagulation and hemorrhagic disorders	76	COLONOSCOPY AND BIOPSY	661	Coagulation & platelet disorders	16	Diseases and Disorders of Blood, Blood Forming Organs and Immunological Disorders	3	Major	Moderate	Medical	Medicare	NA	NA	40003993	137074	NA	0	N	Y	$12730.75	$4252.01	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	50 to 69	147	F	White	Not Span/Hispanic	6	Emergency	Inpatient Rehabilitation Facility	2015	135	Intestinal infection	222	BLOOD TRANSFUSION	248	Major gastrointestinal & peritoneal infections	6	Diseases and Disorders of the Digestive System	4	Extreme	Major	Medical	Medicare	Medicaid	NA	266141	251437	NA	0	N	Y	$17490.31	$9772.47	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	70 or Older	147	F	White	Not Span/Hispanic	10	Emergency	Skilled Nursing Home	2015	157	Acute and unspecified renal failure	222	BLOOD TRANSFUSION	460	RENAL FAILURE	11	Diseases and Disorders of the Kidney and Urinary Tract	4	Extreme	Extreme	Medical	Medicare	Private Health Insurance	NA	266141	276511	NA	0	N	Y	$19586.28	$8822.05	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	18 to 29	147	F	White	Not Span/Hispanic	1	Emergency	Left Against Medical Advice	2015	196	Other pregnancy and delivery including normal	0	NO PROC	561	Postpartum & post abortion diagnoses w/o procedure	14	Pregnancy, Childbirth and the Puerperium	1	Minor	Minor	Medical	Private Health Insurance	NA	NA	256322	NA	NA	0	N	Y	$2203.28	$894.46	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	70 or Older	140	F	White	Not Span/Hispanic	6	Emergency	Skilled Nursing Home	2015	159	Urinary tract infections	0	NO PROC	463	Kidney & urinary tract infections	11	Diseases and Disorders of the Kidney and Urinary Tract	3	Major	Major	Medical	Medicare	NA	NA	170599	NA	NA	0	N	Y	$10387.40	$4716.31	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	50 to 69	147	F	White	Not Span/Hispanic	2	Elective	Home or Self Care	2015	44	Neoplasms of unspecified nature or uncertain behavior	124	HYSTERECTOMY; AB/VAG	513	Uterine & adnexa procedures for non-malignancy except leiomyoma	13	Diseases and Disorders of the Female Reproductive System	1	Minor	Minor	Surgical	Blue Cross/Blue Shield	NA	NA	155651	155651	NA	0	N	N	$15570.16	$12042.57	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	70 or Older	147	F	White	Not Span/Hispanic	6	Emergency	Home w/ Home Health Services	2015	159	Urinary tract infections	54	OT VASC CATH; NOT HEART	463	Kidney & urinary tract infections	11	Diseases and Disorders of the Kidney and Urinary Tract	2	Moderate	Major	Medical	Medicare	NA	NA	161469	161469	NA	0	N	Y	$17509.05	$9587.57	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	30 to 49	147	F	White	Not Span/Hispanic	2	Emergency	Inpatient Rehabilitation Facility	2015	3	Bacterial infection; unspecified site	54	OT VASC CATH; NOT HEART	724	Other infectious & parasitic diseases	18	Infectious and Parasitic Diseases, Systemic or Unspecified Sites	3	Major	Minor	Medical	Medicaid	NA	NA	197563	197563	NA	0	N	Y	$12811.88	$6991.10	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	50 to 69	147	F	White	Not Span/Hispanic	6	Elective	Home w/ Home Health Services	2015	197	Skin and subcutaneous tissue infections	0	NO PROC	383	Cellulitis & other skin infections	9	Diseases and Disorders of the Skin, Subcutaneous Tissue and Breast	2	Moderate	Minor	Medical	Medicare	NA	NA	161469	NA	NA	0	N	N	$10372.37	$5325.48	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	50 to 69	141	F	White	Not Span/Hispanic	3	Emergency	Home or Self Care	2015	657	Mood disorders	0	NO PROC	751	Major depressive disorders & other/unspecified psychoses	19	Mental Diseases and Disorders	2	Moderate	Minor	Medical	Blue Cross/Blue Shield	NA	NA	275408	NA	NA	0	N	Y	$3688.28	$2800.36	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	70 or Older	147	F	White	Not Span/Hispanic	4	Emergency	Skilled Nursing Home	2015	153	Gastrointestinal hemorrhage	92	OTHER BOWEL DX PRCS	253	Other & unspecified gastrointestinal hemorrhage	6	Diseases and Disorders of the Digestive System	3	Major	Extreme	Medical	Medicare	Medicaid	NA	141658	251671	NA	0	N	Y	$11755.70	$4987.86	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	50 to 69	148	F	White	Not Span/Hispanic	6	Emergency	Hosp Basd Medicare Approved Swing Bed	2015	197	Skin and subcutaneous tissue infections	54	OT VASC CATH; NOT HEART	383	Cellulitis & other skin infections	9	Diseases and Disorders of the Skin, Subcutaneous Tissue and Breast	1	Minor	Moderate	Medical	Blue Cross/Blue Shield	NA	NA	266141	252850	NA	0	N	Y	$14615.33	$8883.59	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	50 to 69	147	F	White	Not Span/Hispanic	2	Emergency	Home or Self Care	2015	153	Gastrointestinal hemorrhage	92	OTHER BOWEL DX PRCS	253	Other & unspecified gastrointestinal hemorrhage	6	Diseases and Disorders of the Digestive System	1	Minor	Minor	Medical	Blue Cross/Blue Shield	NA	NA	256322	137074	NA	0	N	Y	$7648.80	$2457.26	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	18 to 29	147	F	White	Not Span/Hispanic	3	Elective	Home or Self Care	2015	184	Early or threatened labor	137	OT PRCS TO ASSIST DELIV	560	Vaginal delivery	14	Pregnancy, Childbirth and the Puerperium	2	Moderate	Minor	Medical	Medicaid	NA	NA	60420192	60420192	NA	0	N	N	$5429.70	$3396.63	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	70 or Older	147	M	White	Not Span/Hispanic	2	Emergency	Home or Self Care	2015	146	Diverticulosis and diverticulitis	0	NO PROC	244	Diverticulitis & diverticulosis	6	Diseases and Disorders of the Digestive System	2	Moderate	Moderate	Medical	Medicare	Blue Cross/Blue Shield	Private Health Insurance	197453	NA	NA	0	N	Y	$4622.00	$1691.56	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	50 to 69	OOS	M	White	Not Span/Hispanic	2	Elective	Short-term Hospital	2015	100	Acute myocardial infarction	47	DX CARDIAC CATHETERIZTN	190	Acute myocardial infarction	5	Diseases and Disorders of the Circulatory System	1	Minor	Minor	Medical	Blue Cross/Blue Shield	NA	NA	271326	183914	NA	0	N	N	$22161.20	$12458.00	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	50 to 69	147	M	White	Not Span/Hispanic	3	Emergency	Home w/ Home Health Services	2015	226	Fracture of neck of femur (hip)	153	HIP REPLACEMENT,TOT/PRT	301	Hip joint replacement	8	Diseases and Disorders of the Musculoskeletal System and Conn Tissue	1	Minor	Minor	Surgical	Blue Cross/Blue Shield	Private Health Insurance	NA	172880	172880	90012432	0	N	Y	$30155.82	$55346.46	Hospital	Not for Profit Corporation
66	Western NY	Cattaraugus	0401001	Olean General Hospital	70 or Older	147	M	White	Not Span/Hispanic	4	Emergency	Skilled Nursing Home	2015	149	Biliary tract disease	0	NO PROC	284	Disorders of gallbladder & biliary tract	7	Diseases and Disorders of the Hepatobiliary System and Pancreas	3	Major	Major	Medical	Medicare	Medicaid	NA	165169	NA	NA	0	N	Y	$13651.03	$5599.37	Hospital	Not for Profit Corporation

3.1 Data Cleaning

# rename Zip.Code...3.digits
colnames(dat)[which(colnames(dat) == "Zip.Code...3.digits")] <- "Zip"

# make Length.of.Stay numeric
dat[which(dat$Length.of.Stay == "120 +"), "Length.of.Stay"] <- "121"
dat$Length.of.Stay <- as.numeric(dat$Length.of.Stay)

# Remove dollar sign from Total Costs and Total Charges and make numeric
dat$Total.Charges <- as.numeric(substring(dat$Total.Charges, 2))
dat$Total.Costs <- as.numeric(substring(dat$Total.Costs, 2))

# Create cost per day variable
dat$Cost.per.Day <- dat$Total.Costs/dat$Length.of.Stay

# Re-order factors
dat$APR.MDC.Code <- factor(dat$APR.MDC.Code, levels = as.character(0:25))

dat$APR.Severity.of.Illness.Description <- factor(dat$APR.Severity.of.Illness.Description, 
    levels = c("Minor", "Moderate", "Major", "Extreme"))

# Remove columns: discharge year is 2015 for all rows provider license numbers
# are many-leveled factors unused in analysis patient disposition information is
# known at end of hospital stay, not at admission
dat <- dat[, which(!(colnames(dat) %in% c("Discharge.Year", "Operating.Certificate.Number", 
    "Attending.Provider.License.Number", "Operating.Provider.License.Number", "Other.Provider.License.Number", 
    "Patient.Disposition")))]

# Look at makeup of dataset
summary(dat)

##   Facility.Id          Health.Service.Area   Hospital.County   
##  1456   :  55896   New York City :1092224   Manhattan: 400991  
##  541    :  47712   Long Island   : 339277   Kings    : 248955  
##  1464   :  47518   Hudson Valley : 245945   Queens   : 197202  
##  1458   :  42997   Capital/Adiron: 167367   Bronx    : 188160  
##  1169   :  42720   Western NY    : 163927   Nassau   : 181164  
##  (Other):2107006   (Other)       : 335109   (Other)  :1127377  
##  NA's   :   2911   NA's          :   2911   NA's     :   2911  
##                                                         Facility.Name    
##  Mount Sinai Hospital                                          :  55896  
##  North Shore University Hospital                               :  47712  
##  New York Presbyterian Hospital - Columbia Presbyterian Center :  47518  
##  New York Presbyterian Hospital - New York Weill Cornell Center:  42997  
##  Montefiore Medical Center - Henry & Lucy Moses Div            :  42720  
##  Maimonides Medical Center                                     :  41909  
##  (Other)                                                       :2068008  
##        Age.Group           Zip          Gender     
##  0 to 17    :352588   112    : 313548   F:1307507  
##  18 to 29   :247223   104    : 224997   M:1039206  
##  30 to 49   :458457   117    : 182030   U:     47  
##  50 to 69   :645004   100    : 170127              
##  70 or Older:643488   113    : 121512              
##                       (Other):1330119              
##                       NA's   :   4427              
##                      Race                     Ethnicity       Length.of.Stay   
##  Black/African American: 444944   Multi-ethnic     :   8693   Min.   :  1.000  
##  Multi-racial          :  22380   Not Span/Hispanic:1954468   1st Qu.:  2.000  
##  Other Race            : 544559   Spanish/Hispanic : 278587   Median :  3.000  
##  White                 :1334877   Unknown          : 105012   Mean   :  5.476  
##                                                               3rd Qu.:  6.000  
##                                                               Max.   :121.000  
##                                                                                
##      Type.of.Admission   CCS.Diagnosis.Code
##  Elective     : 447280   218    : 226813   
##  Emergency    :1488031   2      : 108709   
##  Newborn      : 227100   203    :  63476   
##  Not Available:   1173   108    :  58760   
##  Trauma       :   6394   657    :  56950   
##  Urgent       : 176782   122    :  47082   
##                          (Other):1784970   
##                                                                   CCS.Diagnosis.Description
##  Liveborn                                                                      : 226813    
##  Septicemia (except in labor)                                                  : 108709    
##  Osteoarthritis                                                                :  63476    
##  Congestive heart failure; nonhypertensive                                     :  58760    
##  Mood disorders                                                                :  56950    
##  Pneumonia (except that caused by tuberculosis or sexually transmitted disease):  47082    
##  (Other)                                                                       :1784970    
##  CCS.Procedure.Code           CCS.Procedure.Description  APR.DRG.Code    
##  0      : 610252    NO PROC                : 610252     640    : 198114  
##  231    : 175510    OTHER THERAPEUTIC PRCS : 175510     560    : 147035  
##  137    :  83658    OT PRCS TO ASSIST DELIV:  83658     720    :  94966  
##  228    :  81060    PROPHYLACTIC VAC/INOCUL:  81060     540    :  76059  
##  134    :  74806    CESAREAN SECTION       :  74806     194    :  56375  
##  216    :  74069    RESP INTUB/MECH VENTIL :  74069     139    :  43040  
##  (Other):1247405    (Other)                :1247405     (Other):1731171  
##                                                         APR.DRG.Description 
##  Neonate birthwt >2499g, normal newborn or neonate w other problem: 198114  
##  Vaginal delivery                                                 : 147035  
##  Septicemia & disseminated infections                             :  94966  
##  Cesarean delivery                                                :  76059  
##  Heart failure                                                    :  56375  
##  Other pneumonia                                                  :  43040  
##  (Other)                                                          :1731171  
##   APR.MDC.Code   
##  5      :289531  
##  14     :254079  
##  15     :231854  
##  8      :204675  
##  6      :197654  
##  4      :196486  
##  (Other):972481  
##                                                                       APR.MDC.Description
##  Diseases and Disorders of the Circulatory System                               :289531  
##  Pregnancy, Childbirth and the Puerperium                                       :254079  
##  Newborns and Other Neonates with Conditions Originating in the Perinatal Period:231854  
##  Diseases and Disorders of the Musculoskeletal System and Conn Tissue           :204675  
##  Diseases and Disorders of the Digestive System                                 :197654  
##  Diseases and Disorders of the Respiratory System                               :196486  
##  (Other)                                                                        :972481  
##  APR.Severity.of.Illness.Code APR.Severity.of.Illness.Description
##  0:   112                     Minor   :785526                    
##  1:785526                     Moderate:897251                    
##  2:897251                     Major   :517129                    
##  3:517129                     Extreme :146742                    
##  4:146742                     NA's    :   112                    
##                                                                  
##                                                                  
##  APR.Risk.of.Mortality APR.Medical.Surgical.Description
##  Extreme : 121749      Medical       :1779501          
##  Major   : 335242      Not Applicable:    112          
##  Minor   :1389588      Surgical      : 567147          
##  Moderate: 500069                                      
##  NA's    :    112                                      
##                                                        
##                                                        
##                 Payment.Typology.1                Payment.Typology.2
##  Medicare                :876258   Medicaid                :554720  
##  Medicaid                :717285   Self-Pay                :366081  
##  Private Health Insurance:334558   Medicare                :336787  
##  Blue Cross/Blue Shield  :275552   Private Health Insurance:161646  
##  Self-Pay                : 67879   Blue Cross/Blue Shield  :124393  
##  Miscellaneous/Other     : 28985   (Other)                 : 40787  
##  (Other)                 : 46243   NA's                    :762346  
##                 Payment.Typology.3   Birth.Weight    Abortion.Edit.Indicator
##  Self-Pay                : 479620   Min.   :   0.0   N:2343849              
##  Medicaid                : 124629   1st Qu.:   0.0   Y:   2911              
##  Private Health Insurance:  34861   Median :   0.0                          
##  Blue Cross/Blue Shield  :  21473   Mean   : 326.4                          
##  Medicare                :  18971   3rd Qu.:   0.0                          
##  (Other)                 :  21636   Max.   :9900.0                          
##  NA's                    :1645570                                           
##  Emergency.Department.Indicator Total.Charges      Total.Costs     
##  N: 977695                      Min.   :      0   Min.   :      0  
##  Y:1369065                      1st Qu.:  12027   1st Qu.:   4724  
##                                 Median :  23481   Median :   8791  
##                                 Mean   :  43206   Mean   :  15985  
##                                 3rd Qu.:  46607   3rd Qu.:  16835  
##                                 Max.   :7248391   Max.   :5236615  
##                                                                    
##                                           Facility.Type    
##  Hospital                                        :2296627  
##  Primary Care Hospital - Critical Access Hospital:   9361  
##  NA's                                            :  40772  
##                                                            
##                                                            
##                                                            
##                                                            
##                     Ownership.Type     Cost.per.Day    
##  County                    :   3711   Min.   :      0  
##  Municipality              : 186339   1st Qu.:   1611  
##  Not for Profit Corporation:1979711   Median :   2465  
##  Public Benefit Corporation:  47937   Mean   :   3482  
##  State                     :  88290   3rd Qu.:   4098  
##  NA's                      :  40772   Max.   :1017571  
## 

report_table(head(dat, 50))

Facility.Id	Health.Service.Area	Hospital.County	Facility.Name	Age.Group	Zip	Gender	Race	Ethnicity	Length.of.Stay	Type.of.Admission	CCS.Diagnosis.Code	CCS.Diagnosis.Description	CCS.Procedure.Code	CCS.Procedure.Description	APR.DRG.Code	APR.DRG.Description	APR.MDC.Code	APR.MDC.Description	APR.Severity.of.Illness.Code	APR.Severity.of.Illness.Description	APR.Risk.of.Mortality	APR.Medical.Surgical.Description	Payment.Typology.1	Payment.Typology.2	Payment.Typology.3	Birth.Weight	Abortion.Edit.Indicator	Emergency.Department.Indicator	Total.Charges	Total.Costs	Facility.Type	Ownership.Type	Cost.per.Day
66	Western NY	Cattaraugus	Olean General Hospital	30 to 49	147	F	White	Not Span/Hispanic	5	Emergency	127	Chronic obstructive pulmonary disease and bronchiectasis	0	NO PROC	140	Chronic obstructive pulmonary disease	4	Diseases and Disorders of the Respiratory System	3	Major	Moderate	Medical	Medicare	Medicaid	NA	0	N	Y	18309.20	10309.98	Hospital	Not for Profit Corporation	2061.9960
66	Western NY	Cattaraugus	Olean General Hospital	70 or Older	147	M	White	Not Span/Hispanic	3	Emergency	108	Congestive heart failure; nonhypertensive	58	HEMODIALYSIS	194	Heart failure	5	Diseases and Disorders of the Circulatory System	3	Major	Major	Medical	Medicare	NA	NA	0	N	Y	12310.76	6034.20	Hospital	Not for Profit Corporation	2011.4000
66	Western NY	Cattaraugus	Olean General Hospital	70 or Older	148	F	White	Not Span/Hispanic	9	Emergency	2	Septicemia (except in labor)	222	BLOOD TRANSFUSION	720	Septicemia & disseminated infections	18	Infectious and Parasitic Diseases, Systemic or Unspecified Sites	4	Extreme	Major	Medical	Medicare	NA	NA	0	N	Y	48242.20	20494.93	Hospital	Not for Profit Corporation	2277.2144
66	Western NY	Cattaraugus	Olean General Hospital	50 to 69	OOS	F	White	Not Span/Hispanic	2	Elective	100	Acute myocardial infarction	47	DX CARDIAC CATHETERIZTN	190	Acute myocardial infarction	5	Diseases and Disorders of the Circulatory System	2	Moderate	Moderate	Medical	Medicaid	NA	NA	0	N	N	12794.77	7369.54	Hospital	Not for Profit Corporation	3684.7700
66	Western NY	Cattaraugus	Olean General Hospital	70 or Older	147	F	White	Not Span/Hispanic	4	Emergency	100	Acute myocardial infarction	0	NO PROC	190	Acute myocardial infarction	5	Diseases and Disorders of the Circulatory System	2	Moderate	Moderate	Medical	Medicare	NA	NA	0	N	Y	10292.68	4001.00	Hospital	Not for Profit Corporation	1000.2500
66	Western NY	Cattaraugus	Olean General Hospital	18 to 29	141	M	White	Not Span/Hispanic	7	Emergency	130	Pleurisy; pneumothorax; pulmonary collapse	39	INCISION OF PLEURA	143	Other respiratory diagnoses except signs, symptoms & minor diagnoses	4	Diseases and Disorders of the Respiratory System	1	Minor	Minor	Medical	Medicaid	NA	NA	0	N	Y	14177.09	7711.28	Hospital	Not for Profit Corporation	1101.6114
66	Western NY	Cattaraugus	Olean General Hospital	50 to 69	141	M	White	Not Span/Hispanic	9	Emergency	660	Alcohol-related disorders	231	OTHER THERAPEUTIC PRCS	280	Alcoholic liver disease	7	Diseases and Disorders of the Hepatobiliary System and Pancreas	3	Major	Major	Medical	Medicare	NA	NA	0	N	Y	21448.73	9511.37	Hospital	Not for Profit Corporation	1056.8189
66	Western NY	Cattaraugus	Olean General Hospital	0 to 17	147	F	White	Not Span/Hispanic	3	Newborn	218	Liveborn	0	NO PROC	640	Neonate birthwt >2499g, normal newborn or neonate w other problem	15	Newborns and Other Neonates with Conditions Originating in the Perinatal Period	1	Minor	Minor	Medical	Medicaid	NA	NA	3400	N	N	2393.10	1327.02	Hospital	Not for Profit Corporation	442.3400
66	Western NY	Cattaraugus	Olean General Hospital	0 to 17	147	F	White	Not Span/Hispanic	4	Newborn	218	Liveborn	0	NO PROC	640	Neonate birthwt >2499g, normal newborn or neonate w other problem	15	Newborns and Other Neonates with Conditions Originating in the Perinatal Period	2	Moderate	Minor	Medical	Medicaid	NA	NA	2900	N	N	4191.00	2136.17	Hospital	Not for Profit Corporation	534.0425
66	Western NY	Cattaraugus	Olean General Hospital	70 or Older	147	F	White	Not Span/Hispanic	4	Elective	204	Other non-traumatic joint disorders	152	ARTHROPLASTY KNEE	302	Knee joint replacement	8	Diseases and Disorders of the Musculoskeletal System and Conn Tissue	1	Minor	Minor	Surgical	Medicare	Private Health Insurance	NA	0	N	N	29514.01	59253.25	Hospital	Not for Profit Corporation	14813.3125
66	Western NY	Cattaraugus	Olean General Hospital	0 to 17	147	F	White	Not Span/Hispanic	1	Newborn	218	Liveborn	0	NO PROC	640	Neonate birthwt >2499g, normal newborn or neonate w other problem	15	Newborns and Other Neonates with Conditions Originating in the Perinatal Period	1	Minor	Minor	Medical	Medicaid	NA	NA	2700	N	N	813.50	459.49	Hospital	Not for Profit Corporation	459.4900
66	Western NY	Cattaraugus	Olean General Hospital	50 to 69	140	M	White	Not Span/Hispanic	4	Emergency	2	Septicemia (except in labor)	0	NO PROC	720	Septicemia & disseminated infections	18	Infectious and Parasitic Diseases, Systemic or Unspecified Sites	3	Major	Major	Medical	Medicare	Blue Cross/Blue Shield	NA	0	N	Y	10114.85	4943.62	Hospital	Not for Profit Corporation	1235.9050
66	Western NY	Cattaraugus	Olean General Hospital	0 to 17	147	M	White	Not Span/Hispanic	2	Newborn	218	Liveborn	115	CIRCUMCISION	640	Neonate birthwt >2499g, normal newborn or neonate w other problem	15	Newborns and Other Neonates with Conditions Originating in the Perinatal Period	1	Minor	Minor	Medical	Medicaid	NA	NA	2600	N	N	1510.00	929.25	Hospital	Not for Profit Corporation	464.6250
66	Western NY	Cattaraugus	Olean General Hospital	50 to 69	147	M	White	Not Span/Hispanic	2	Emergency	129	Aspiration pneumonitis; food/vomitus	0	NO PROC	137	Major respiratory infections & inflammations	4	Diseases and Disorders of the Respiratory System	3	Major	Moderate	Medical	Medicaid	NA	NA	0	N	Y	7330.35	2502.54	Hospital	Not for Profit Corporation	1251.2700
66	Western NY	Cattaraugus	Olean General Hospital	0 to 17	147	F	White	Not Span/Hispanic	2	Newborn	218	Liveborn	0	NO PROC	640	Neonate birthwt >2499g, normal newborn or neonate w other problem	15	Newborns and Other Neonates with Conditions Originating in the Perinatal Period	2	Moderate	Minor	Medical	Medicaid	NA	NA	2900	N	N	1528.50	907.69	Hospital	Not for Profit Corporation	453.8450
66	Western NY	Cattaraugus	Olean General Hospital	0 to 17	148	M	White	Not Span/Hispanic	1	Newborn	218	Liveborn	115	CIRCUMCISION	640	Neonate birthwt >2499g, normal newborn or neonate w other problem	15	Newborns and Other Neonates with Conditions Originating in the Perinatal Period	1	Minor	Minor	Medical	Medicaid	Medicaid	NA	3200	N	N	851.50	496.77	Hospital	Not for Profit Corporation	496.7700
66	Western NY	Cattaraugus	Olean General Hospital	18 to 29	147	F	White	Not Span/Hispanic	3	Elective	187	Malposition; malpresentation	134	CESAREAN SECTION	540	Cesarean delivery	14	Pregnancy, Childbirth and the Puerperium	1	Minor	Minor	Surgical	Medicaid	NA	NA	0	N	N	8550.41	4645.93	Hospital	Not for Profit Corporation	1548.6433
66	Western NY	Cattaraugus	Olean General Hospital	70 or Older	147	F	White	Not Span/Hispanic	10	Emergency	51	Other endocrine disorders	0	NO PROC	424	Other endocrine disorders	10	Endocrine, Nutritional and Metabolic Diseases and Disorders	3	Major	Major	Medical	Medicare	NA	NA	0	N	Y	17076.26	9286.99	Hospital	Not for Profit Corporation	928.6990
66	Western NY	Cattaraugus	Olean General Hospital	50 to 69	147	F	White	Not Span/Hispanic	13	Emergency	2	Septicemia (except in labor)	54	OT VASC CATH; NOT HEART	720	Septicemia & disseminated infections	18	Infectious and Parasitic Diseases, Systemic or Unspecified Sites	4	Extreme	Extreme	Medical	Medicare	Private Health Insurance	NA	0	N	Y	58394.67	40505.88	Hospital	Not for Profit Corporation	3115.8369
66	Western NY	Cattaraugus	Olean General Hospital	70 or Older	OOS	F	White	Not Span/Hispanic	7	Emergency	127	Chronic obstructive pulmonary disease and bronchiectasis	0	NO PROC	140	Chronic obstructive pulmonary disease	4	Diseases and Disorders of the Respiratory System	2	Moderate	Moderate	Medical	Medicare	Federal/State/Local/VA	NA	0	N	Y	17623.18	8901.52	Hospital	Not for Profit Corporation	1271.6457
66	Western NY	Cattaraugus	Olean General Hospital	50 to 69	147	M	White	Not Span/Hispanic	2	Emergency	103	Pulmonary heart disease	0	NO PROC	134	Pulmonary embolism	4	Diseases and Disorders of the Respiratory System	1	Minor	Minor	Medical	Medicaid	NA	NA	0	N	Y	8016.13	2608.73	Hospital	Not for Profit Corporation	1304.3650
66	Western NY	Cattaraugus	Olean General Hospital	30 to 49	147	F	White	Not Span/Hispanic	7	Emergency	657	Mood disorders	0	NO PROC	753	Bipolar disorders	19	Mental Diseases and Disorders	2	Moderate	Minor	Medical	Medicaid	NA	NA	0	N	Y	7380.68	9880.01	Hospital	Not for Profit Corporation	1411.4300
66	Western NY	Cattaraugus	Olean General Hospital	0 to 17	147	M	White	Not Span/Hispanic	3	Newborn	218	Liveborn	115	CIRCUMCISION	640	Neonate birthwt >2499g, normal newborn or neonate w other problem	15	Newborns and Other Neonates with Conditions Originating in the Perinatal Period	1	Minor	Minor	Medical	Blue Cross/Blue Shield	NA	NA	3200	N	N	1964.00	1261.62	Hospital	Not for Profit Corporation	420.5400
66	Western NY	Cattaraugus	Olean General Hospital	50 to 69	147	M	White	Not Span/Hispanic	4	Emergency	11	Cancer of head and neck	71	GASTROSTOMY; TEMP/PERM	110	Ear, nose, mouth, throat, cranial/facial malignancies	3	Ear, Nose, Mouth, Throat and Craniofacial Diseases and Disorders	3	Major	Moderate	Medical	Private Health Insurance	Federal/State/Local/VA	NA	0	N	Y	7568.00	5248.66	Hospital	Not for Profit Corporation	1312.1650
66	Western NY	Cattaraugus	Olean General Hospital	70 or Older	148	M	White	Not Span/Hispanic	6	Emergency	50	Diabetes mellitus with complications	0	NO PROC	468	Other kidney & urinary tract diagnoses, signs & symptoms	11	Diseases and Disorders of the Kidney and Urinary Tract	3	Major	Major	Medical	Medicare	Private Health Insurance	NA	0	N	Y	10902.98	5216.32	Hospital	Not for Profit Corporation	869.3867
66	Western NY	Cattaraugus	Olean General Hospital	50 to 69	147	F	White	Not Span/Hispanic	4	Emergency	127	Chronic obstructive pulmonary disease and bronchiectasis	216	RESP INTUB/MECH VENTIL	140	Chronic obstructive pulmonary disease	4	Diseases and Disorders of the Respiratory System	3	Major	Extreme	Medical	Medicare	NA	NA	0	N	Y	14544.13	6380.94	Hospital	Not for Profit Corporation	1595.2350
66	Western NY	Cattaraugus	Olean General Hospital	0 to 17	141	F	White	Not Span/Hispanic	2	Newborn	218	Liveborn	0	NO PROC	640	Neonate birthwt >2499g, normal newborn or neonate w other problem	15	Newborns and Other Neonates with Conditions Originating in the Perinatal Period	1	Minor	Minor	Medical	Blue Cross/Blue Shield	NA	NA	2500	N	N	1216.42	811.52	Hospital	Not for Profit Corporation	405.7600
66	Western NY	Cattaraugus	Olean General Hospital	30 to 49	148	F	White	Not Span/Hispanic	2	Emergency	657	Mood disorders	0	NO PROC	753	Bipolar disorders	19	Mental Diseases and Disorders	1	Minor	Minor	Medical	Federal/State/Local/VA	NA	NA	0	N	Y	2415.05	1876.09	Hospital	Not for Profit Corporation	938.0450
66	Western NY	Cattaraugus	Olean General Hospital	30 to 49	147	F	White	Not Span/Hispanic	1	Elective	196	Other pregnancy and delivery including normal	137	OT PRCS TO ASSIST DELIV	541	Vaginal delivery w sterilization &/or D&C	14	Pregnancy, Childbirth and the Puerperium	1	Minor	Minor	Surgical	Federal/State/Local/VA	NA	NA	0	N	N	4256.44	3224.37	Hospital	Not for Profit Corporation	3224.3700
66	Western NY	Cattaraugus	Olean General Hospital	18 to 29	147	M	White	Not Span/Hispanic	5	Emergency	657	Mood disorders	0	NO PROC	751	Major depressive disorders & other/unspecified psychoses	19	Mental Diseases and Disorders	1	Minor	Minor	Medical	Blue Cross/Blue Shield	Medicaid	NA	0	N	Y	5176.78	6235.63	Hospital	Not for Profit Corporation	1247.1260
66	Western NY	Cattaraugus	Olean General Hospital	50 to 69	147	F	White	Not Span/Hispanic	9	Emergency	42	Secondary malignancies	231	OTHER THERAPEUTIC PRCS	952	Nonextensive procedure unrelated to principal diagnosis	4	Diseases and Disorders of the Respiratory System	3	Major	Major	Surgical	Medicare	Medicaid	NA	0	N	Y	22783.03	12623.80	Hospital	Not for Profit Corporation	1402.6444
66	Western NY	Cattaraugus	Olean General Hospital	50 to 69	147	F	White	Not Span/Hispanic	2	Emergency	127	Chronic obstructive pulmonary disease and bronchiectasis	0	NO PROC	140	Chronic obstructive pulmonary disease	4	Diseases and Disorders of the Respiratory System	2	Moderate	Moderate	Medical	Medicare	NA	NA	0	N	Y	15927.38	5406.24	Hospital	Not for Profit Corporation	2703.1200
66	Western NY	Cattaraugus	Olean General Hospital	70 or Older	147	M	White	Not Span/Hispanic	3	Emergency	62	Coagulation and hemorrhagic disorders	76	COLONOSCOPY AND BIOPSY	661	Coagulation & platelet disorders	16	Diseases and Disorders of Blood, Blood Forming Organs and Immunological Disorders	3	Major	Moderate	Medical	Medicare	NA	NA	0	N	Y	12730.75	4252.01	Hospital	Not for Profit Corporation	1417.3367
66	Western NY	Cattaraugus	Olean General Hospital	50 to 69	147	F	White	Not Span/Hispanic	6	Emergency	135	Intestinal infection	222	BLOOD TRANSFUSION	248	Major gastrointestinal & peritoneal infections	6	Diseases and Disorders of the Digestive System	4	Extreme	Major	Medical	Medicare	Medicaid	NA	0	N	Y	17490.31	9772.47	Hospital	Not for Profit Corporation	1628.7450
66	Western NY	Cattaraugus	Olean General Hospital	70 or Older	147	F	White	Not Span/Hispanic	10	Emergency	157	Acute and unspecified renal failure	222	BLOOD TRANSFUSION	460	RENAL FAILURE	11	Diseases and Disorders of the Kidney and Urinary Tract	4	Extreme	Extreme	Medical	Medicare	Private Health Insurance	NA	0	N	Y	19586.28	8822.05	Hospital	Not for Profit Corporation	882.2050
66	Western NY	Cattaraugus	Olean General Hospital	18 to 29	147	F	White	Not Span/Hispanic	1	Emergency	196	Other pregnancy and delivery including normal	0	NO PROC	561	Postpartum & post abortion diagnoses w/o procedure	14	Pregnancy, Childbirth and the Puerperium	1	Minor	Minor	Medical	Private Health Insurance	NA	NA	0	N	Y	2203.28	894.46	Hospital	Not for Profit Corporation	894.4600
66	Western NY	Cattaraugus	Olean General Hospital	70 or Older	140	F	White	Not Span/Hispanic	6	Emergency	159	Urinary tract infections	0	NO PROC	463	Kidney & urinary tract infections	11	Diseases and Disorders of the Kidney and Urinary Tract	3	Major	Major	Medical	Medicare	NA	NA	0	N	Y	10387.40	4716.31	Hospital	Not for Profit Corporation	786.0517
66	Western NY	Cattaraugus	Olean General Hospital	50 to 69	147	F	White	Not Span/Hispanic	2	Elective	44	Neoplasms of unspecified nature or uncertain behavior	124	HYSTERECTOMY; AB/VAG	513	Uterine & adnexa procedures for non-malignancy except leiomyoma	13	Diseases and Disorders of the Female Reproductive System	1	Minor	Minor	Surgical	Blue Cross/Blue Shield	NA	NA	0	N	N	15570.16	12042.57	Hospital	Not for Profit Corporation	6021.2850
66	Western NY	Cattaraugus	Olean General Hospital	70 or Older	147	F	White	Not Span/Hispanic	6	Emergency	159	Urinary tract infections	54	OT VASC CATH; NOT HEART	463	Kidney & urinary tract infections	11	Diseases and Disorders of the Kidney and Urinary Tract	2	Moderate	Major	Medical	Medicare	NA	NA	0	N	Y	17509.05	9587.57	Hospital	Not for Profit Corporation	1597.9283
66	Western NY	Cattaraugus	Olean General Hospital	30 to 49	147	F	White	Not Span/Hispanic	2	Emergency	3	Bacterial infection; unspecified site	54	OT VASC CATH; NOT HEART	724	Other infectious & parasitic diseases	18	Infectious and Parasitic Diseases, Systemic or Unspecified Sites	3	Major	Minor	Medical	Medicaid	NA	NA	0	N	Y	12811.88	6991.10	Hospital	Not for Profit Corporation	3495.5500
66	Western NY	Cattaraugus	Olean General Hospital	50 to 69	147	F	White	Not Span/Hispanic	6	Elective	197	Skin and subcutaneous tissue infections	0	NO PROC	383	Cellulitis & other skin infections	9	Diseases and Disorders of the Skin, Subcutaneous Tissue and Breast	2	Moderate	Minor	Medical	Medicare	NA	NA	0	N	N	10372.37	5325.48	Hospital	Not for Profit Corporation	887.5800
66	Western NY	Cattaraugus	Olean General Hospital	50 to 69	141	F	White	Not Span/Hispanic	3	Emergency	657	Mood disorders	0	NO PROC	751	Major depressive disorders & other/unspecified psychoses	19	Mental Diseases and Disorders	2	Moderate	Minor	Medical	Blue Cross/Blue Shield	NA	NA	0	N	Y	3688.28	2800.36	Hospital	Not for Profit Corporation	933.4533
66	Western NY	Cattaraugus	Olean General Hospital	70 or Older	147	F	White	Not Span/Hispanic	4	Emergency	153	Gastrointestinal hemorrhage	92	OTHER BOWEL DX PRCS	253	Other & unspecified gastrointestinal hemorrhage	6	Diseases and Disorders of the Digestive System	3	Major	Extreme	Medical	Medicare	Medicaid	NA	0	N	Y	11755.70	4987.86	Hospital	Not for Profit Corporation	1246.9650
66	Western NY	Cattaraugus	Olean General Hospital	50 to 69	148	F	White	Not Span/Hispanic	6	Emergency	197	Skin and subcutaneous tissue infections	54	OT VASC CATH; NOT HEART	383	Cellulitis & other skin infections	9	Diseases and Disorders of the Skin, Subcutaneous Tissue and Breast	1	Minor	Moderate	Medical	Blue Cross/Blue Shield	NA	NA	0	N	Y	14615.33	8883.59	Hospital	Not for Profit Corporation	1480.5983
66	Western NY	Cattaraugus	Olean General Hospital	50 to 69	147	F	White	Not Span/Hispanic	2	Emergency	153	Gastrointestinal hemorrhage	92	OTHER BOWEL DX PRCS	253	Other & unspecified gastrointestinal hemorrhage	6	Diseases and Disorders of the Digestive System	1	Minor	Minor	Medical	Blue Cross/Blue Shield	NA	NA	0	N	Y	7648.80	2457.26	Hospital	Not for Profit Corporation	1228.6300
66	Western NY	Cattaraugus	Olean General Hospital	18 to 29	147	F	White	Not Span/Hispanic	3	Elective	184	Early or threatened labor	137	OT PRCS TO ASSIST DELIV	560	Vaginal delivery	14	Pregnancy, Childbirth and the Puerperium	2	Moderate	Minor	Medical	Medicaid	NA	NA	0	N	N	5429.70	3396.63	Hospital	Not for Profit Corporation	1132.2100
66	Western NY	Cattaraugus	Olean General Hospital	70 or Older	147	M	White	Not Span/Hispanic	2	Emergency	146	Diverticulosis and diverticulitis	0	NO PROC	244	Diverticulitis & diverticulosis	6	Diseases and Disorders of the Digestive System	2	Moderate	Moderate	Medical	Medicare	Blue Cross/Blue Shield	Private Health Insurance	0	N	Y	4622.00	1691.56	Hospital	Not for Profit Corporation	845.7800
66	Western NY	Cattaraugus	Olean General Hospital	50 to 69	OOS	M	White	Not Span/Hispanic	2	Elective	100	Acute myocardial infarction	47	DX CARDIAC CATHETERIZTN	190	Acute myocardial infarction	5	Diseases and Disorders of the Circulatory System	1	Minor	Minor	Medical	Blue Cross/Blue Shield	NA	NA	0	N	N	22161.20	12458.00	Hospital	Not for Profit Corporation	6229.0000
66	Western NY	Cattaraugus	Olean General Hospital	50 to 69	147	M	White	Not Span/Hispanic	3	Emergency	226	Fracture of neck of femur (hip)	153	HIP REPLACEMENT,TOT/PRT	301	Hip joint replacement	8	Diseases and Disorders of the Musculoskeletal System and Conn Tissue	1	Minor	Minor	Surgical	Blue Cross/Blue Shield	Private Health Insurance	NA	0	N	Y	30155.82	55346.46	Hospital	Not for Profit Corporation	18448.8200
66	Western NY	Cattaraugus	Olean General Hospital	70 or Older	147	M	White	Not Span/Hispanic	4	Emergency	149	Biliary tract disease	0	NO PROC	284	Disorders of gallbladder & biliary tract	7	Diseases and Disorders of the Hepatobiliary System and Pancreas	3	Major	Major	Medical	Medicare	Medicaid	NA	0	N	Y	13651.03	5599.37	Hospital	Not for Profit Corporation	1399.8425

4 Preliminary Data Exploration

4.1 MDC Codes

The following codes are Major Diagnostic Categories (MDC) that generally correspond to a major organ system. The original 1-23 MDC codes are grouped by primary diagnosis. In 1986 MDC codes were expanded to include MDC Codes 0 (Pre-MDC), 24 (Human Immunodeficiency Virus or HIV), and 25 (Multiple Significant Trauma), the latter of which, unlike codes 1-23, are based on both the primary and secondary diagnosis. Patients are assigned Pre-MDC when their Diagnosis-Related Group (DRG) is based on a procedure, mostly transplants (heart, liver, intestinal, bone marrow, etc.) and tracheostomies in this dataset, instead of a primary diagnosis and are grouped separately due to the very resource intensive nature of these procedures which may be used to treat numerous different diagnoses across MDCs [8].

# get row of first instance of each APR.MDC.Code in order
mdc_codes <- dat[match(levels(dat$APR.MDC.Code), dat$APR.MDC.Code), c("APR.MDC.Code", 
    "APR.MDC.Description")]

report_table(mdc_codes, w = "650px", ec = "position: center; display: block; margin: auto;")

APR.MDC.Code	APR.MDC.Description
0	Pre-MDC or Ungroupable
1	Diseases and Disorders of the Nervous System
2	Diseases and Disorders of the Eye
3	Ear, Nose, Mouth, Throat and Craniofacial Diseases and Disorders
4	Diseases and Disorders of the Respiratory System
5	Diseases and Disorders of the Circulatory System
6	Diseases and Disorders of the Digestive System
7	Diseases and Disorders of the Hepatobiliary System and Pancreas
8	Diseases and Disorders of the Musculoskeletal System and Conn Tissue
9	Diseases and Disorders of the Skin, Subcutaneous Tissue and Breast
10	Endocrine, Nutritional and Metabolic Diseases and Disorders
11	Diseases and Disorders of the Kidney and Urinary Tract
12	Diseases and Disorders of the Male Reproductive System
13	Diseases and Disorders of the Female Reproductive System
14	Pregnancy, Childbirth and the Puerperium
15	Newborns and Other Neonates with Conditions Originating in the Perinatal Period
16	Diseases and Disorders of Blood, Blood Forming Organs and Immunological Disorders
17	Lymphatic, Hematopoietic, Other Malignancies, Chemotherapy and Radiotherapy
18	Infectious and Parasitic Diseases, Systemic or Unspecified Sites
19	Mental Diseases and Disorders
20	Alcohol/Drug Use and Alcohol/Drug Induced Organic Mental Disorders
21	Poisonings, Toxic Effects, Other Injuries and Other Complications of Treatment
22	Burns
23	Rehabilitation, Aftercare, Other Factors Influencing Health Status and Other Health Service Contacts
24	Human Immunodeficiency Virus Infections
25	Multiple Significant Trauma

4.2 Figures

LOS

Length of stay goes from 1 to 121 (previously 120+) but the majority of the data lies between 1 and 30. With the most patients having stayed 2 days.

report_plot(ggplot(dat) + geom_histogram_interactive(aes(x = Length.of.Stay, tooltip = ..count..), 
    binwidth = 1, fill = "#69b3a2", color = "#e9ecef", alpha = 0.9) + ggtitle("Distribution of Length of Stay") + 
    xlab("Length of Stay") + ylab("Frequency") + scale_x_continuous(breaks = c(1, 
    10, 20, 30, 40), limits = c(0, 40)) + scale_y_continuous(labels = scales::comma))

---

LOS by Age

Median length of stay increases as age group increases. The interquartile range of length of stay also increases as age group increases.

ggplot(dat, aes(x = Age.Group, y = Length.of.Stay, fill = Age.Group)) + geom_boxplot() + 
    theme(legend.position = "none") + ggtitle("Length of Stay by Age Group") + xlab("Age Group") + 
    ylab("Length of Stay") + scale_y_continuous(breaks = c(1, 10, 20), limits = c(0, 
    20))

---

Avg LOS by MDC

The longest average length of stay among MDC groups was the 0 MDC group which corresponds to Pre-MDC or Ungroupable. As discussed earlier, the Pre-MDC group is primarily composed of transplant patients which explains the longer average time spent as an inpatient.

report_plot(ggplot(dat, aes(x = APR.MDC.Code, y = Length.of.Stay, tooltip = APR.MDC.Description)) + 
    geom_bar_interactive(stat = "summary", fun = "mean", fill = "#69b3a2") + ggtitle("Average Length of Stay by APR MDC Code") + 
    xlab("APR MDC Code") + ylab("Average Length of Stay"))

---

Avg LOS by Severity

As severity of illness increases, average length of stay increases. Cases labeled as extreme stay for an average of 15 days.

report_plot(ggplot(dat, aes(x = APR.Severity.of.Illness.Description, y = Length.of.Stay, 
    fill = APR.Severity.of.Illness.Description)) + geom_bar_interactive(stat = "summary", 
    fun = "mean") + theme(legend.position = "none") + ggtitle("Length of Stay by Severity of Illness") + 
    xlab("Severity of Illness") + ylab("Average Length of Stay"))

---

Avg LOS by Ownership

Ownership type was one of the variables merged from the second dataset which gave additional information about facility type. There is a clear distinction in mean length of stay between the different ownership types with the longest average length of stay being for a Public Benefit Corporation (PBC). A PBC is a type of for-profit entity. Municipality owned hospitals, which are run by the local government, have the second largest average length of stay

Similarly, the boxplot shows a higher median length of stay for PBC and a larger spread.

ggplot(subset(dat, !is.na(Ownership.Type)), aes(x = reorder(Ownership.Type, Length.of.Stay), 
    y = Length.of.Stay, fill = Ownership.Type)) + stat_summary(fun = "mean", geom = "bar") + 
    theme(legend.position = "none") + ggtitle("Length of Stay by Ownership Type") + 
    xlab("Ownership Type") + ylab("Average Length of Stay")

ggplot(dat, aes(x = Ownership.Type, y = Length.of.Stay, fill = Ownership.Type)) + 
    geom_boxplot() + theme(legend.position = "none") + ggtitle("Length of Stay by Ownership Type") + 
    xlab("Ownership Type") + ylab("Length of Stay") + scale_y_continuous(breaks = c(1, 
    10, 20), limits = c(0, 20))

---

Avg LOS by Type

The average length of stay is greater in hospitals than in Critical Access Hospitals. Critical Access Hospitals are rural hospitals overseen by the Centers for Medicare and Medicaid Services (CMS) that meet the following criteria: 25 or fewer acute care inpatient beds, at least 35 miles from the nearest hospital, keep the average length of stay for the year at 96 hours or less for acute care patients, and have emergency care services available 24/7. By keeping their status as a Critical Access Hospital, they receive certain benefits from CMS which would Critical Access Hopsitals to keep the length of stay lower in order to keep their status. [9].

ggplot(dat, aes(x = Facility.Type, y = Length.of.Stay, fill = Facility.Type)) + stat_summary(fun = "mean", 
    geom = "bar") + theme(legend.position = "none") + ggtitle("Average Length of stay by Facility Type") + 
    xlab("Facility Type") + ylab("Average Length of Stay")

---

Avg CPD by Admission

Cost per day is highest in patients with elective procedures and cases of trauma.

ggplot(dat, aes(x = Type.of.Admission, y = Cost.per.Day, fill = Type.of.Admission)) + 
    stat_summary(fun = "mean", geom = "bar") + theme(legend.position = "none") + 
    ggtitle("Cost per Day by Type of Admission") + xlab("Admission Type") + ylab("Average Cost per Day")

---

Avg CPD by Age

Average cost per day increased as age group increased with the highest average cost in the age group from 50 to 69. Surprisingly, average cost for those 70 or older was less than both age groups of 30 to 49 and 50 to 69.

ggplot(dat, aes(x = Age.Group, y = Cost.per.Day, fill = Age.Group)) + stat_summary(fun = "mean", 
    geom = "bar") + theme(legend.position = "none") + ggtitle("Cost per day by Age Group") + 
    xlab("Age Group") + ylab("Average Cost per day")

---

Avg CPD by MDC

Diseases and Disorders of the Male Reproductive System (MDC Code 12), Diseases and Disorders of the Musculoskeletal System and Connective Tissue (MDC Code 8), Diseases and Disorders of the Female Reproductive System (MDC Code 13) had the highest average costs per day.

report_plot(ggplot(dat, aes(x = APR.MDC.Code, y = Cost.per.Day, tooltip = APR.MDC.Description)) + 
    geom_bar_interactive(stat = "summary", fun = "mean", fill = "#69b3a2") + ggtitle("Average Cost per day by APR MDC Code") + 
    xlab("APR MDC Code") + ylab("Average Cost per day"))

---

Avg CPD by Ownership

Municipality owned hospitals’ cost per patient per day is at least $1000 more on average than the other four ownership types.

ggplot(dat, aes(x = Ownership.Type, y = Cost.per.Day, fill = Ownership.Type)) + stat_summary(fun = "mean", 
    geom = "bar") + theme(legend.position = "none") + ggtitle("Average Cost per day by Ownership Type") + 
    xlab("Ownership Type") + ylab("Average Cost per day")

---

4.3 Birth Weight

We chose to filter out observations that were related to pregnancy and newborn data as there are unique characteristics of their features. The birthweight feature, for example, was only reported for newborns. For all other observations, the birthweight was recorded as 0.

In the figure below, we see that over 2 million observations have birth weight equal to 0.

# report_plot( ggplot(dat, aes(x = Birth.Weight)) + geom_histogram_interactive(
# aes(tooltip = ..count..), fill = '#69b3a2', alpha = 0.9) +
# ggtitle('Distribution of Birth Weight') + xlab('Birth Weight (grams)') +
# ylab('Frequency'))


report_plot(ggplot(dat) + geom_histogram_interactive(aes(x = Birth.Weight, tooltip = ..count..), 
    binwidth = 1, fill = "#69b3a2", color = "#e9ecef", alpha = 0.9) + ggtitle("Distribution of Birth Weight") + 
    xlab("Birth Weight (grams)") + ylab("Frequency"))

4.4 Abortion Indicator

Due to confidentiality concerns, some columns were censored if the discharge record for that observation contained any potential indication of abortion, including but not limited to: elective abortion procedures, miscarriages, ectopic pregnancies, etc.

All observations with missing data for Facility.Id, Health Service Area, and Hospital County also had Abortion.Edit.Indicator = ‘Y’. The plot below shows the MDC codes that had observations where Abortion.Edit.Indicator was equal to ‘Y’. The majority of these observations were when APR MDC Code was equal to 14 which corresponds to the MDC ‘Pregnancy, Childbirth And Puerperium’.

report_plot(ggplot(subset(dat, dat$Abortion.Edit.Indicator == "Y"), aes(x = APR.MDC.Code, 
    tooltip = APR.MDC.Description)) + geom_bar_interactive(fill = "#69b3a2") + ggtitle("Frequency of Observations Related to Abortion by MDC Code") + 
    xlab("APR MDC Code") + ylab("Frequency") + theme(legend.position = "none") + 
    scale_y_continuous(labels = scales::comma))

4.5 Data Filtering

Rows meeting any of the following criteria were filtered:

• APR.DRG.Code corresponding to a APR.DRG.Description containing OB-GYN-related terms
• CCS.Diagnosis.Code corresponding to a CCS.Diagnosis.Description containing OB-GYN-related terms
• APR.MDC.Code = 14 [‘Pregnancy, Childbirth And Puerperium’]
• APR.MDC.Code = 15 [‘Newborn And Other Neonates (Perinatal Period)’]
• Abortion.Edit.Indicator = ‘Y’
• Type.of.Admission = ‘Newborn’
• Birth.Weight > 0

# get unique codes, descriptions
aprdrg <- unique(dat[, c("APR.DRG.Code", "APR.DRG.Description")])
aprdrg <- aprdrg[order(aprdrg$APR.DRG.Code), ]
rownames(aprdrg) <- NULL

ccs <- unique(dat[, c("CCS.Diagnosis.Code", "CCS.Diagnosis.Description")])
ccs <- ccs[order(ccs$CCS.Diagnosis.Code), ]
rownames(ccs) <- NULL

# terms for filtering out OB-related
obgyn_terms <- paste0(c("abortion", "amniot", "birth", "C-section", "delivery", "fetal", 
    "fetopelvic", "labor", "liveborn", "malposition", "natal", "neonat", "obstetric", 
    "OB-related", "partum", "pregnancy", "umbilical cord complication"), collapse = "|")
exclude_terms <- paste0(c("non-obstetric", "except in labor"), collapse = "|")

filter_obgyn <- function(x) {
    return(grep(exclude_terms, grep(obgyn_terms, x, ignore.case = TRUE, value = TRUE), 
        ignore.case = TRUE, value = TRUE, invert = TRUE))
}

# get APR.DRG.Code values to filter out
aprdrg_obgyn_codes <- aprdrg[aprdrg$APR.DRG.Description %in% filter_obgyn(aprdrg$APR.DRG.Description), 
    "APR.DRG.Code"]

# get CCS.Diagnosis.Code values to filter out
ccs_obgyn_codes <- ccs[ccs$CCS.Diagnosis.Description %in% filter_obgyn(ccs$CCS.Diagnosis.Description), 
    "CCS.Diagnosis.Code"]

# filter dat to include only non-obgyn data, non-neonate data
obgyn_rows <- with(dat, which(CCS.Diagnosis.Code %in% ccs_obgyn_codes | APR.DRG.Code %in% 
    aprdrg_obgyn_codes | APR.MDC.Code == 14 | APR.MDC.Code == 15 | Abortion.Edit.Indicator == 
    "Y" | Type.of.Admission == "Newborn" | Birth.Weight > 0))
dat <- dat[-obgyn_rows, ]

# remove columns
dat <- dat[, which(!(colnames(dat) %in% c("Abortion.Edit.Indicator", "Birth.Weight")))]

After filtering, there there are 1856727 observations remaining.

5 Medicare Patient Data

Due to the amount of computing power that it would take to analyze the whole dataset, we chose to subset the data by if any of a patient’s payment types (primary, secondary, or tertiary) were Medicare. 874,388 patients had Medicare as their primary payment type, and 55,333 additional patients had Medicare as either their secondary or tertiary payment type for a total of 929,721 patients.

# Subset to only medicare patients
medicare_rows <- with(dat, which(Payment.Typology.1 == "Medicare" | Payment.Typology.2 == 
    "Medicare" | Payment.Typology.3 == "Medicare"))
dat <- dat[medicare_rows, ]

# drop unused levels
dat <- droplevels(dat)

5.1 Figures

LOS

The distribution of length of stay in the subset with only patients with Medicare resembles the overall distribution, but the largest frequency of length of stay in this subset is 3 days.

report_plot(ggplot(dat) + geom_histogram_interactive(aes(x = Length.of.Stay, tooltip = after_stat(count)), 
    binwidth = 1, fill = "#69b3a2", color = "#e9ecef", alpha = 0.9) + ggtitle("Distribution of Length of Stay") + 
    xlab("Length of Stay") + ylab("Frequency") + scale_x_continuous(breaks = c(1, 
    10, 20, 30, 40), limits = c(0, 40)) + scale_y_continuous(labels = scales::comma))

---

MDC

The greatest number of medicare patients were admitted due to Diseases and Disorders of the Circulatory System (MDC Code 5) then Diseases and Disorders of the Respiratory System (MDC Code 4) and Diseases and Disorders of the Musculoskeletal System and Connective Tissue (MDC Code 8).

report_plot(ggplot(dat, aes(x = APR.MDC.Code, tooltip = APR.MDC.Description)) + geom_bar_interactive(fill = "#69b3a2", 
    color = "#e9ecef", alpha = 0.9) + ggtitle("Frequency of APR MDC Code in Medicare Patients") + 
    xlab("APR MDC Code") + ylab("Frequency"))

---

Age

As expected, the majority of patients with Medicare are 70 or older and also many in the 50 to 69 age group.

report_plot(ggplot(dat, aes(x = Age.Group)) + geom_bar_interactive(aes(tooltip = after_stat(count)), 
    fill = "#69b3a2", color = "#e9ecef", alpha = 0.9) + ggtitle("Frequency of Individuals with Medicare by Age Group") + 
    xlab("Medicare") + ylab("Frequency") + scale_y_continuous(labels = scales::comma))

---

6 Analysis

# Split train and test set
set.seed(123)
train_rows <- caret::createDataPartition(y = dat$Length.of.Stay, p = 0.7, list = FALSE)
train <- dat[train_rows, ]
test <- dat[-train_rows, ]

6.1 Evaluation Metrics

We will be using the same evaluation metrics used in the literature for the assessment of similar length of stay prediction models: \(R^2\) [1], mean absolute error (MAE) [1,2], mean relative error (MRE) [2], and root mean squared error (RMSE) [2].

\[ MAE = \frac {\sum_{i = 1}^{n} |\hat y_i - y_i|}{n} \]

\[ MRE = \frac {\sum_{i = 1}^{n} (|\hat y_i - y_i|/y_i)}{n}\]

\[ RMSE = \sqrt\frac {\sum_{i = 1}^{n} (\hat y_i - y_i)^2}{n}\] where \(\hat y_i\) is the predicted value for length of stay or cost per dayand \(y_i\) is the actual value for length of stay or cost per day.

# Error functions
MAE <- function(pred, actual) {
    mean(abs(actual - pred))
}
MRE <- function(pred, actual) {
    mean(abs(actual - pred)/actual)
}
RMSE <- function(pred, actual) {
    sqrt(mean((actual - pred)^2))
}

evaluate_model <- function(model, test, response) {
    
    actual <- test[[response]]
    pred <- predict(model, test)
    
    # Remove rows when response == 0; MRE = infinity for those observations
    if (any(test[[response]] == 0)) {
        test_mre <- test[!test[[response]] == 0, ]
        pred_mre <- predict(model, test_mre)
        actual_mre <- test_mre[[response]]
    } else {
        pred_mre <- pred
        actual_mre <- actual
    }
    
    return(c(`Mean Absolute Error` = round(MAE(pred, actual), digits = 2), `Mean Relative Error` = round(MRE(pred_mre, 
        actual_mre), digits = 2), `Root Mean Squared Error` = round(RMSE(pred, actual), 
        digits = 2)))
}

6.2 Length of Stay

In the following models, we consider the following variables to predict length of stay.

---

Column	Description
Age.Group	Age in years at time of discharge grouped into 0 to 17, 18 to 29, 30 to 49, 50 to 69, 70+
Gender	Male, Female, Unknown
Race	Black/African American, Multi, Other Race, Unknown, White.
Ethnicity	Spanish/Hispanic Origin, Not of Spanish/Hispanic Origin, Multi, Unknown.
Type.of.Admission	Elective, Emergency, Newborn, Not Available, Trauma, Urgent.
APR.MDC.Code	0-25
APR.Severity.of.Illness.Code	Minor (1), Moderate (2), Major (3) , Extreme (4).
APR.Risk.of.Mortality	Minor (1), Moderate (2), Major (3) , Extreme (4).
Ownership.Type	County, Municipality, Not for Profit Corporation, Public Benefit Corporation, State
Facility.Type	Hospital, Primary Care Hospital - Critical Access Hospital
Emergency.Department.Indicator	If the record contained an Emergency Department revenue code of 045X, the indicator is set to “Y”, otherwise it will be “N”.
Health.Service.Area	8 service areas represented
Hospital.County	57 Hospital counties represented

---

All of these variables are recorded at admission so no future information such as Total Cost is included in the model.

6.2.1 Linear Regression

We wanted to focus our efforts in predicting length of stay through regression methods and not classification methods because knowing the exact number of days a patient would need to stay would be overall more useful than knowing a range of days a patient may stay. We start with a simple linear regression as our base model although we acknowledge that fundamentally, this is not the proper model that we want to use to model length of stay.

linearReg <- lm(Length.of.Stay ~ Age.Group + Gender + Race + Ethnicity + Type.of.Admission + 
    APR.MDC.Code + APR.Severity.of.Illness.Code + APR.Risk.of.Mortality + Ownership.Type + 
    Facility.Type + Emergency.Department.Indicator + Health.Service.Area + Hospital.County, 
    data = train)
summary(linearReg)

## 
## Call:
## lm(formula = Length.of.Stay ~ Age.Group + Gender + Race + Ethnicity + 
##     Type.of.Admission + APR.MDC.Code + APR.Severity.of.Illness.Code + 
##     APR.Risk.of.Mortality + Ownership.Type + Facility.Type + 
##     Emergency.Department.Indicator + Health.Service.Area + Hospital.County, 
##     data = train)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -24.266  -2.921  -0.990   1.348 117.851 
## 
## Coefficients: (7 not defined because of singularities)
##                                                               Estimate
## (Intercept)                                                    1.84581
## Age.Group18 to 29                                              2.23548
## Age.Group30 to 49                                              2.10698
## Age.Group50 to 69                                              2.22973
## Age.Group70 or Older                                           1.77959
## GenderM                                                       -0.06179
## GenderU                                                       -0.15782
## RaceMulti-racial                                              -0.05776
## RaceOther Race                                                -0.51203
## RaceWhite                                                     -0.39648
## EthnicityNot Span/Hispanic                                     0.27230
## EthnicitySpanish/Hispanic                                     -0.08276
## EthnicityUnknown                                               0.24512
## Type.of.AdmissionEmergency                                    -0.58307
## Type.of.AdmissionNot Available                                -1.01670
## Type.of.AdmissionTrauma                                        0.41914
## Type.of.AdmissionUrgent                                        0.83830
## APR.MDC.Code2                                                 -0.79959
## APR.MDC.Code3                                                 -0.93989
## APR.MDC.Code4                                                 -0.63769
## APR.MDC.Code5                                                 -1.11459
## APR.MDC.Code6                                                 -0.08713
## APR.MDC.Code7                                                 -0.26711
## APR.MDC.Code8                                                 -0.06009
## APR.MDC.Code9                                                  0.04053
## APR.MDC.Code10                                                -1.29699
## APR.MDC.Code11                                                -0.98647
## APR.MDC.Code12                                                -1.10269
## APR.MDC.Code13                                                -0.83214
## APR.MDC.Code16                                                -0.68514
## APR.MDC.Code17                                                 1.97804
## APR.MDC.Code18                                                -0.58273
## APR.MDC.Code19                                                 9.70821
## APR.MDC.Code20                                                 1.90188
## APR.MDC.Code21                                                -1.38021
## APR.MDC.Code22                                                 5.07095
## APR.MDC.Code23                                                 4.26049
## APR.MDC.Code24                                                -0.60053
## APR.MDC.Code25                                                 0.93427
## APR.Severity.of.Illness.Code2                                  1.10670
## APR.Severity.of.Illness.Code3                                  3.16984
## APR.Severity.of.Illness.Code4                                  9.06343
## APR.Risk.of.MortalityMajor                                    -1.40676
## APR.Risk.of.MortalityMinor                                    -3.26966
## APR.Risk.of.MortalityModerate                                 -2.47810
## Ownership.TypeMunicipality                                     4.55932
## Ownership.TypeNot for Profit Corporation                       3.21298
## Ownership.TypePublic Benefit Corporation                       5.31600
## Ownership.TypeState                                            3.51789
## Facility.TypePrimary Care Hospital - Critical Access Hospital -0.54996
## Emergency.Department.IndicatorY                               -0.27390
## Health.Service.AreaCentral NY                                 -1.33232
## Health.Service.AreaFinger Lakes                               -2.83891
## Health.Service.AreaHudson Valley                               0.46858
## Health.Service.AreaLong Island                                 0.11763
## Health.Service.AreaNew York City                               0.44096
## Health.Service.AreaSouthern Tier                              -1.28723
## Health.Service.AreaWestern NY                                  2.29715
## Hospital.CountyAllegany                                       -3.42785
## Hospital.CountyBronx                                           0.11297
## Hospital.CountyBroome                                          0.52047
## Hospital.CountyCattaraugus                                    -4.07397
## Hospital.CountyCayuga                                         -0.29408
## Hospital.CountyChautauqua                                     -3.68636
## Hospital.CountyChemung                                         2.02711
## Hospital.CountyChenango                                             NA
## Hospital.CountyClinton                                        -0.06400
## Hospital.CountyColumbia                                        0.22025
## Hospital.CountyCortland                                       -0.50571
## Hospital.CountyDelaware                                       -0.46812
## Hospital.CountyDutchess                                       -1.61482
## Hospital.CountyErie                                           -3.07511
## Hospital.CountyEssex                                          -0.64575
## Hospital.CountyFranklin                                       -1.80682
## Hospital.CountyFulton                                         -1.38847
## Hospital.CountyGenesee                                        -3.84128
## Hospital.CountyHerkimer                                        0.65630
## Hospital.CountyJefferson                                       1.23635
## Hospital.CountyKings                                          -0.13454
## Hospital.CountyLewis                                           3.00428
## Hospital.CountyLivingston                                      2.78739
## Hospital.CountyMadison                                        -0.10136
## Hospital.CountyManhattan                                      -0.48479
## Hospital.CountyMonroe                                          3.01853
## Hospital.CountyMontgomery                                     -1.25763
## Hospital.CountyNassau                                          0.25982
## Hospital.CountyNiagara                                        -2.50530
## Hospital.CountyOneida                                          0.79021
## Hospital.CountyOnondaga                                        1.19327
## Hospital.CountyOntario                                         2.04596
## Hospital.CountyOrange                                         -1.22661
## Hospital.CountyOrleans                                        -1.58778
## Hospital.CountyOswego                                          0.10542
## Hospital.CountyOtsego                                         -0.42158
## Hospital.CountyPutnam                                         -2.48192
## Hospital.CountyQueens                                          0.11431
## Hospital.CountyRensselaer                                     -0.23273
## Hospital.CountyRichmond                                             NA
## Hospital.CountyRockland                                       -0.76132
## Hospital.CountySaratoga                                        0.12449
## Hospital.CountySchenectady                                    -0.28084
## Hospital.CountySchuyler                                        2.64624
## Hospital.CountySt Lawrence                                     0.09196
## Hospital.CountySteuben                                         1.04735
## Hospital.CountySuffolk                                              NA
## Hospital.CountySullivan                                       -1.35045
## Hospital.CountyTompkins                                             NA
## Hospital.CountyUlster                                         -0.71042
## Hospital.CountyWarren                                         -0.45330
## Hospital.CountyWayne                                           1.34869
## Hospital.CountyWestchester                                          NA
## Hospital.CountyWyoming                                              NA
## Hospital.CountyYates                                                NA
##                                                               Std. Error
## (Intercept)                                                      1.79931
## Age.Group18 to 29                                                0.44303
## Age.Group30 to 49                                                0.43226
## Age.Group50 to 69                                                0.43063
## Age.Group70 or Older                                             0.43064
## GenderM                                                          0.01868
## GenderU                                                          7.35333
## RaceMulti-racial                                                 0.10400
## RaceOther Race                                                   0.03540
## RaceWhite                                                        0.02818
## EthnicityNot Span/Hispanic                                       0.18919
## EthnicitySpanish/Hispanic                                        0.19161
## EthnicityUnknown                                                 0.19552
## Type.of.AdmissionEmergency                                       0.04401
## Type.of.AdmissionNot Available                                   0.39477
## Type.of.AdmissionTrauma                                          0.21100
## Type.of.AdmissionUrgent                                          0.04806
## APR.MDC.Code2                                                    0.25397
## APR.MDC.Code3                                                    0.09109
## APR.MDC.Code4                                                    0.04232
## APR.MDC.Code5                                                    0.03858
## APR.MDC.Code6                                                    0.04359
## APR.MDC.Code7                                                    0.06509
## APR.MDC.Code8                                                    0.04343
## APR.MDC.Code9                                                    0.06393
## APR.MDC.Code10                                                   0.06051
## APR.MDC.Code11                                                   0.04776
## APR.MDC.Code12                                                   0.13021
## APR.MDC.Code13                                                   0.12689
## APR.MDC.Code16                                                   0.07977
## APR.MDC.Code17                                                   0.10052
## APR.MDC.Code18                                                   0.04615
## APR.MDC.Code19                                                   0.06196
## APR.MDC.Code20                                                   0.09397
## APR.MDC.Code21                                                   0.09700
## APR.MDC.Code22                                                   0.48111
## APR.MDC.Code23                                                   0.06708
## APR.MDC.Code24                                                   0.19960
## APR.MDC.Code25                                                   0.23877
## APR.Severity.of.Illness.Code2                                    0.02955
## APR.Severity.of.Illness.Code3                                    0.03704
## APR.Severity.of.Illness.Code4                                    0.05580
## APR.Risk.of.MortalityMajor                                       0.04547
## APR.Risk.of.MortalityMinor                                       0.05615
## APR.Risk.of.MortalityModerate                                    0.05051
## Ownership.TypeMunicipality                                       1.73478
## Ownership.TypeNot for Profit Corporation                         1.73413
## Ownership.TypePublic Benefit Corporation                         1.73583
## Ownership.TypeState                                              1.73500
## Facility.TypePrimary Care Hospital - Critical Access Hospital    0.24278
## Emergency.Department.IndicatorY                                  0.03735
## Health.Service.AreaCentral NY                                    0.17230
## Health.Service.AreaFinger Lakes                                  0.48471
## Health.Service.AreaHudson Valley                                 0.06724
## Health.Service.AreaLong Island                                   0.06306
## Health.Service.AreaNew York City                                 0.07773
## Health.Service.AreaSouthern Tier                                 0.30699
## Health.Service.AreaWestern NY                                    1.75606
## Hospital.CountyAllegany                                          1.77752
## Hospital.CountyBronx                                             0.06954
## Hospital.CountyBroome                                            0.31256
## Hospital.CountyCattaraugus                                       1.76296
## Hospital.CountyCayuga                                            0.23443
## Hospital.CountyChautauqua                                        1.75993
## Hospital.CountyChemung                                           0.49322
## Hospital.CountyChenango                                               NA
## Hospital.CountyClinton                                           0.14127
## Hospital.CountyColumbia                                          0.16128
## Hospital.CountyCortland                                          0.25781
## Hospital.CountyDelaware                                          0.48678
## Hospital.CountyDutchess                                          0.08271
## Hospital.CountyErie                                              1.75574
## Hospital.CountyEssex                                             0.53186
## Hospital.CountyFranklin                                          0.19326
## Hospital.CountyFulton                                            0.23890
## Hospital.CountyGenesee                                           1.76667
## Hospital.CountyHerkimer                                          0.45624
## Hospital.CountyJefferson                                         0.22276
## Hospital.CountyKings                                             0.06617
## Hospital.CountyLewis                                             1.80853
## Hospital.CountyLivingston                                        0.55063
## Hospital.CountyMadison                                           0.26063
## Hospital.CountyManhattan                                         0.06350
## Hospital.CountyMonroe                                            0.48363
## Hospital.CountyMontgomery                                        0.15476
## Hospital.CountyNassau                                            0.04711
## Hospital.CountyNiagara                                           1.75781
## Hospital.CountyOneida                                            0.17969
## Hospital.CountyOnondaga                                          0.17234
## Hospital.CountyOntario                                           0.49477
## Hospital.CountyOrange                                            0.07868
## Hospital.CountyOrleans                                           1.80369
## Hospital.CountyOswego                                            0.24939
## Hospital.CountyOtsego                                            0.12090
## Hospital.CountyPutnam                                            0.15278
## Hospital.CountyQueens                                            0.06826
## Hospital.CountyRensselaer                                        0.12881
## Hospital.CountyRichmond                                               NA
## Hospital.CountyRockland                                          0.08744
## Hospital.CountySaratoga                                          0.13852
## Hospital.CountySchenectady                                       0.10382
## Hospital.CountySchuyler                                          0.58526
## Hospital.CountySt Lawrence                                       0.21144
## Hospital.CountySteuben                                           0.50472
## Hospital.CountySuffolk                                                NA
## Hospital.CountySullivan                                          0.20612
## Hospital.CountyTompkins                                               NA
## Hospital.CountyUlster                                            0.11837
## Hospital.CountyWarren                                            0.11510
## Hospital.CountyWayne                                             0.51197
## Hospital.CountyWestchester                                            NA
## Hospital.CountyWyoming                                                NA
## Hospital.CountyYates                                                  NA
##                                                               t value Pr(>|t|)
## (Intercept)                                                     1.026 0.304967
## Age.Group18 to 29                                               5.046 4.52e-07
## Age.Group30 to 49                                               4.874 1.09e-06
## Age.Group50 to 69                                               5.178 2.25e-07
## Age.Group70 or Older                                            4.132 3.59e-05
## GenderM                                                        -3.308 0.000941
## GenderU                                                        -0.021 0.982877
## RaceMulti-racial                                               -0.555 0.578635
## RaceOther Race                                                -14.464  < 2e-16
## RaceWhite                                                     -14.068  < 2e-16
## EthnicityNot Span/Hispanic                                      1.439 0.150081
## EthnicitySpanish/Hispanic                                      -0.432 0.665798
## EthnicityUnknown                                                1.254 0.209967
## Type.of.AdmissionEmergency                                    -13.249  < 2e-16
## Type.of.AdmissionNot Available                                 -2.575 0.010011
## Type.of.AdmissionTrauma                                         1.986 0.046984
## Type.of.AdmissionUrgent                                        17.443  < 2e-16
## APR.MDC.Code2                                                  -3.148 0.001642
## APR.MDC.Code3                                                 -10.318  < 2e-16
## APR.MDC.Code4                                                 -15.069  < 2e-16
## APR.MDC.Code5                                                 -28.889  < 2e-16
## APR.MDC.Code6                                                  -1.999 0.045647
## APR.MDC.Code7                                                  -4.104 4.07e-05
## APR.MDC.Code8                                                  -1.384 0.166487
## APR.MDC.Code9                                                   0.634 0.526036
## APR.MDC.Code10                                                -21.436  < 2e-16
## APR.MDC.Code11                                                -20.655  < 2e-16
## APR.MDC.Code12                                                 -8.468  < 2e-16
## APR.MDC.Code13                                                 -6.558 5.46e-11
## APR.MDC.Code16                                                 -8.588  < 2e-16
## APR.MDC.Code17                                                 19.677  < 2e-16
## APR.MDC.Code18                                                -12.628  < 2e-16
## APR.MDC.Code19                                                156.693  < 2e-16
## APR.MDC.Code20                                                 20.239  < 2e-16
## APR.MDC.Code21                                                -14.228  < 2e-16
## APR.MDC.Code22                                                 10.540  < 2e-16
## APR.MDC.Code23                                                 63.517  < 2e-16
## APR.MDC.Code24                                                 -3.009 0.002624
## APR.MDC.Code25                                                  3.913 9.12e-05
## APR.Severity.of.Illness.Code2                                  37.454  < 2e-16
## APR.Severity.of.Illness.Code3                                  85.579  < 2e-16
## APR.Severity.of.Illness.Code4                                 162.430  < 2e-16
## APR.Risk.of.MortalityMajor                                    -30.941  < 2e-16
## APR.Risk.of.MortalityMinor                                    -58.235  < 2e-16
## APR.Risk.of.MortalityModerate                                 -49.066  < 2e-16
## Ownership.TypeMunicipality                                      2.628 0.008584
## Ownership.TypeNot for Profit Corporation                        1.853 0.063913
## Ownership.TypePublic Benefit Corporation                        3.063 0.002195
## Ownership.TypeState                                             2.028 0.042601
## Facility.TypePrimary Care Hospital - Critical Access Hospital  -2.265 0.023497
## Emergency.Department.IndicatorY                                -7.334 2.24e-13
## Health.Service.AreaCentral NY                                  -7.732 1.06e-14
## Health.Service.AreaFinger Lakes                                -5.857 4.72e-09
## Health.Service.AreaHudson Valley                                6.968 3.21e-12
## Health.Service.AreaLong Island                                  1.865 0.062115
## Health.Service.AreaNew York City                                5.673 1.41e-08
## Health.Service.AreaSouthern Tier                               -4.193 2.75e-05
## Health.Service.AreaWestern NY                                   1.308 0.190829
## Hospital.CountyAllegany                                        -1.928 0.053800
## Hospital.CountyBronx                                            1.625 0.104256
## Hospital.CountyBroome                                           1.665 0.095875
## Hospital.CountyCattaraugus                                     -2.311 0.020840
## Hospital.CountyCayuga                                          -1.254 0.209683
## Hospital.CountyChautauqua                                      -2.095 0.036206
## Hospital.CountyChemung                                          4.110 3.96e-05
## Hospital.CountyChenango                                            NA       NA
## Hospital.CountyClinton                                         -0.453 0.650505
## Hospital.CountyColumbia                                         1.366 0.172050
## Hospital.CountyCortland                                        -1.962 0.049813
## Hospital.CountyDelaware                                        -0.962 0.336225
## Hospital.CountyDutchess                                       -19.524  < 2e-16
## Hospital.CountyErie                                            -1.751 0.079867
## Hospital.CountyEssex                                           -1.214 0.224702
## Hospital.CountyFranklin                                        -9.349  < 2e-16
## Hospital.CountyFulton                                          -5.812 6.17e-09
## Hospital.CountyGenesee                                         -2.174 0.029683
## Hospital.CountyHerkimer                                         1.439 0.150292
## Hospital.CountyJefferson                                        5.550 2.86e-08
## Hospital.CountyKings                                           -2.033 0.042014
## Hospital.CountyLewis                                            1.661 0.096679
## Hospital.CountyLivingston                                       5.062 4.15e-07
## Hospital.CountyMadison                                         -0.389 0.697362
## Hospital.CountyManhattan                                       -7.634 2.27e-14
## Hospital.CountyMonroe                                           6.241 4.34e-10
## Hospital.CountyMontgomery                                      -8.126 4.44e-16
## Hospital.CountyNassau                                           5.515 3.49e-08
## Hospital.CountyNiagara                                         -1.425 0.154089
## Hospital.CountyOneida                                           4.398 1.09e-05
## Hospital.CountyOnondaga                                         6.924 4.40e-12
## Hospital.CountyOntario                                          4.135 3.55e-05
## Hospital.CountyOrange                                         -15.590  < 2e-16
## Hospital.CountyOrleans                                         -0.880 0.378701
## Hospital.CountyOswego                                           0.423 0.672527
## Hospital.CountyOtsego                                          -3.487 0.000488
## Hospital.CountyPutnam                                         -16.245  < 2e-16
## Hospital.CountyQueens                                           1.674 0.094042
## Hospital.CountyRensselaer                                      -1.807 0.070791
## Hospital.CountyRichmond                                            NA       NA
## Hospital.CountyRockland                                        -8.707  < 2e-16
## Hospital.CountySaratoga                                         0.899 0.368813
## Hospital.CountySchenectady                                     -2.705 0.006829
## Hospital.CountySchuyler                                         4.522 6.14e-06
## Hospital.CountySt Lawrence                                      0.435 0.663630
## Hospital.CountySteuben                                          2.075 0.037977
## Hospital.CountySuffolk                                             NA       NA
## Hospital.CountySullivan                                        -6.552 5.70e-11
## Hospital.CountyTompkins                                            NA       NA
## Hospital.CountyUlster                                          -6.002 1.95e-09
## Hospital.CountyWarren                                          -3.938 8.20e-05
## Hospital.CountyWayne                                            2.634 0.008431
## Hospital.CountyWestchester                                         NA       NA
## Hospital.CountyWyoming                                             NA       NA
## Hospital.CountyYates                                               NA       NA
##                                                                  
## (Intercept)                                                      
## Age.Group18 to 29                                             ***
## Age.Group30 to 49                                             ***
## Age.Group50 to 69                                             ***
## Age.Group70 or Older                                          ***
## GenderM                                                       ***
## GenderU                                                          
## RaceMulti-racial                                                 
## RaceOther Race                                                ***
## RaceWhite                                                     ***
## EthnicityNot Span/Hispanic                                       
## EthnicitySpanish/Hispanic                                        
## EthnicityUnknown                                                 
## Type.of.AdmissionEmergency                                    ***
## Type.of.AdmissionNot Available                                *  
## Type.of.AdmissionTrauma                                       *  
## Type.of.AdmissionUrgent                                       ***
## APR.MDC.Code2                                                 ** 
## APR.MDC.Code3                                                 ***
## APR.MDC.Code4                                                 ***
## APR.MDC.Code5                                                 ***
## APR.MDC.Code6                                                 *  
## APR.MDC.Code7                                                 ***
## APR.MDC.Code8                                                    
## APR.MDC.Code9                                                    
## APR.MDC.Code10                                                ***
## APR.MDC.Code11                                                ***
## APR.MDC.Code12                                                ***
## APR.MDC.Code13                                                ***
## APR.MDC.Code16                                                ***
## APR.MDC.Code17                                                ***
## APR.MDC.Code18                                                ***
## APR.MDC.Code19                                                ***
## APR.MDC.Code20                                                ***
## APR.MDC.Code21                                                ***
## APR.MDC.Code22                                                ***
## APR.MDC.Code23                                                ***
## APR.MDC.Code24                                                ** 
## APR.MDC.Code25                                                ***
## APR.Severity.of.Illness.Code2                                 ***
## APR.Severity.of.Illness.Code3                                 ***
## APR.Severity.of.Illness.Code4                                 ***
## APR.Risk.of.MortalityMajor                                    ***
## APR.Risk.of.MortalityMinor                                    ***
## APR.Risk.of.MortalityModerate                                 ***
## Ownership.TypeMunicipality                                    ** 
## Ownership.TypeNot for Profit Corporation                      .  
## Ownership.TypePublic Benefit Corporation                      ** 
## Ownership.TypeState                                           *  
## Facility.TypePrimary Care Hospital - Critical Access Hospital *  
## Emergency.Department.IndicatorY                               ***
## Health.Service.AreaCentral NY                                 ***
## Health.Service.AreaFinger Lakes                               ***
## Health.Service.AreaHudson Valley                              ***
## Health.Service.AreaLong Island                                .  
## Health.Service.AreaNew York City                              ***
## Health.Service.AreaSouthern Tier                              ***
## Health.Service.AreaWestern NY                                    
## Hospital.CountyAllegany                                       .  
## Hospital.CountyBronx                                             
## Hospital.CountyBroome                                         .  
## Hospital.CountyCattaraugus                                    *  
## Hospital.CountyCayuga                                            
## Hospital.CountyChautauqua                                     *  
## Hospital.CountyChemung                                        ***
## Hospital.CountyChenango                                          
## Hospital.CountyClinton                                           
## Hospital.CountyColumbia                                          
## Hospital.CountyCortland                                       *  
## Hospital.CountyDelaware                                          
## Hospital.CountyDutchess                                       ***
## Hospital.CountyErie                                           .  
## Hospital.CountyEssex                                             
## Hospital.CountyFranklin                                       ***
## Hospital.CountyFulton                                         ***
## Hospital.CountyGenesee                                        *  
## Hospital.CountyHerkimer                                          
## Hospital.CountyJefferson                                      ***
## Hospital.CountyKings                                          *  
## Hospital.CountyLewis                                          .  
## Hospital.CountyLivingston                                     ***
## Hospital.CountyMadison                                           
## Hospital.CountyManhattan                                      ***
## Hospital.CountyMonroe                                         ***
## Hospital.CountyMontgomery                                     ***
## Hospital.CountyNassau                                         ***
## Hospital.CountyNiagara                                           
## Hospital.CountyOneida                                         ***
## Hospital.CountyOnondaga                                       ***
## Hospital.CountyOntario                                        ***
## Hospital.CountyOrange                                         ***
## Hospital.CountyOrleans                                           
## Hospital.CountyOswego                                            
## Hospital.CountyOtsego                                         ***
## Hospital.CountyPutnam                                         ***
## Hospital.CountyQueens                                         .  
## Hospital.CountyRensselaer                                     .  
## Hospital.CountyRichmond                                          
## Hospital.CountyRockland                                       ***
## Hospital.CountySaratoga                                          
## Hospital.CountySchenectady                                    ** 
## Hospital.CountySchuyler                                       ***
## Hospital.CountySt Lawrence                                       
## Hospital.CountySteuben                                        *  
## Hospital.CountySuffolk                                           
## Hospital.CountySullivan                                       ***
## Hospital.CountyTompkins                                          
## Hospital.CountyUlster                                         ***
## Hospital.CountyWarren                                         ***
## Hospital.CountyWayne                                          ** 
## Hospital.CountyWestchester                                       
## Hospital.CountyWyoming                                           
## Hospital.CountyYates                                             
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.353 on 646418 degrees of freedom
##   (4282 observations deleted due to missingness)
## Multiple R-squared:  0.2083, Adjusted R-squared:  0.2081 
## F-statistic:  1619 on 105 and 646418 DF,  p-value: < 2.2e-16

R_squared = round(summary(linearReg)$r.squared, 4)

# Evaluate linear regression model
eval_LOS_linear <- evaluate_model(linearReg, test, "Length.of.Stay")

## Error in model.frame.default(Terms, newdata, na.action = na.action, xlev = object$xlevels): factor Hospital.County has new levels Schoharie

Note that 7 coefficients are not defined due to singularities. The undefined factors are all from within the hospital county variable. We believe that this is due to the nested structure of the data. Hospital county can directly predict hospital service area because the hospital county variable is nested within the hospital service area. This is another reason that simple linear regression is not the best model for this data.

The \(R^2\) value for the simple linear regression on the training data is 0.2083.

6.2.2 Poisson Model

When you look at thet possible values of length of stay, you see that length of stay can only be integer values greater than 1. Linear regression, on the other hand, will give you continuous values from -infinty to infinity. Therefore, our next step was to model length of stay as a Poisson regression which models count data. This still isn’t quite the right model as a normal Poisson can take on values of 0. Since this is inpatient data, there will never be a patient who has a length of stay of 0.

Poi <- glm(Length.of.Stay ~ Age.Group + Gender + Race + Ethnicity + Type.of.Admission + 
    APR.MDC.Code + APR.Severity.of.Illness.Code + APR.Risk.of.Mortality + Ownership.Type + 
    Facility.Type + Emergency.Department.Indicator + Health.Service.Area + Hospital.County, 
    family = Poisson(link = "log"), data = train)
summary(Poi)

## 
## Call:
## glm(formula = Length.of.Stay ~ Age.Group + Gender + Race + Ethnicity + 
##     Type.of.Admission + APR.MDC.Code + APR.Severity.of.Illness.Code + 
##     APR.Risk.of.Mortality + Ownership.Type + Facility.Type + 
##     Emergency.Department.Indicator + Health.Service.Area + Hospital.County, 
##     family = Poisson(link = "log"), data = train)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -9.9458  -1.3762  -0.5119   0.5400  25.1050  
## 
## Coefficients: (7 not defined because of singularities)
##                                                                 Estimate
## (Intercept)                                                    0.6651407
## Age.Group18 to 29                                              0.6118670
## Age.Group30 to 49                                              0.5741457
## Age.Group50 to 69                                              0.5620829
## Age.Group70 or Older                                           0.4884654
## GenderM                                                       -0.0088477
## GenderU                                                       -0.3109675
## RaceMulti-racial                                              -0.0092244
## RaceOther Race                                                -0.0764085
## RaceWhite                                                     -0.0581423
## EthnicityNot Span/Hispanic                                     0.0508672
## EthnicitySpanish/Hispanic                                     -0.0023940
## EthnicityUnknown                                               0.0469941
## Type.of.AdmissionEmergency                                    -0.1003854
## Type.of.AdmissionNot Available                                -0.1566012
## Type.of.AdmissionTrauma                                        0.0290503
## Type.of.AdmissionUrgent                                        0.0863633
## APR.MDC.Code2                                                 -0.1547136
## APR.MDC.Code3                                                 -0.1781237
## APR.MDC.Code4                                                 -0.0929028
## APR.MDC.Code5                                                 -0.1825256
## APR.MDC.Code6                                                 -0.0131599
## APR.MDC.Code7                                                 -0.0453772
## APR.MDC.Code8                                                  0.0023971
## APR.MDC.Code9                                                  0.0148520
## APR.MDC.Code10                                                -0.2263665
## APR.MDC.Code11                                                -0.1457051
## APR.MDC.Code12                                                -0.2064952
## APR.MDC.Code13                                                -0.1379889
## APR.MDC.Code16                                                -0.1155443
## APR.MDC.Code17                                                 0.2242619
## APR.MDC.Code18                                                -0.0751799
## APR.MDC.Code19                                                 1.1161450
## APR.MDC.Code20                                                 0.3466617
## APR.MDC.Code21                                                -0.2318183
## APR.MDC.Code22                                                 0.5165509
## APR.MDC.Code23                                                 0.5112926
## APR.MDC.Code24                                                -0.1049417
## APR.MDC.Code25                                                 0.0862924
## APR.Severity.of.Illness.Code2                                  0.2701772
## APR.Severity.of.Illness.Code3                                  0.6156490
## APR.Severity.of.Illness.Code4                                  1.1419976
## APR.Risk.of.MortalityMajor                                    -0.1563404
## APR.Risk.of.MortalityMinor                                    -0.4934566
## APR.Risk.of.MortalityModerate                                 -0.3433385
## Ownership.TypeMunicipality                                     0.7533472
## Ownership.TypeNot for Profit Corporation                       0.5662248
## Ownership.TypePublic Benefit Corporation                       0.8396867
## Ownership.TypeState                                            0.6147820
## Facility.TypePrimary Care Hospital - Critical Access Hospital -0.2180760
## Emergency.Department.IndicatorY                               -0.0388687
## Health.Service.AreaCentral NY                                 -0.2067186
## Health.Service.AreaFinger Lakes                               -0.4030761
## Health.Service.AreaHudson Valley                               0.0634730
## Health.Service.AreaLong Island                                 0.0140725
## Health.Service.AreaNew York City                               0.0629664
## Health.Service.AreaSouthern Tier                              -0.2825358
## Health.Service.AreaWestern NY                                  0.4263442
## Hospital.CountyAllegany                                       -0.6375210
## Hospital.CountyBronx                                           0.0125592
## Hospital.CountyBroome                                          0.1548404
## Hospital.CountyCattaraugus                                    -0.7198953
## Hospital.CountyCayuga                                         -0.0593305
## Hospital.CountyChautauqua                                     -0.6344370
## Hospital.CountyChemung                                         0.2790725
## Hospital.CountyChenango                                               NA
## Hospital.CountyClinton                                        -0.0012826
## Hospital.CountyColumbia                                        0.0294518
## Hospital.CountyCortland                                       -0.1078135
## Hospital.CountyDelaware                                       -0.0421928
## Hospital.CountyDutchess                                       -0.2412427
## Hospital.CountyErie                                           -0.5544911
## Hospital.CountyEssex                                          -0.1460775
## Hospital.CountyFranklin                                       -0.3103679
## Hospital.CountyFulton                                         -0.2925608
## Hospital.CountyGenesee                                        -0.7275779
## Hospital.CountyHerkimer                                        0.1837849
## Hospital.CountyJefferson                                       0.2005189
## Hospital.CountyKings                                          -0.0214253
## Hospital.CountyLewis                                           0.5211828
## Hospital.CountyLivingston                                      0.3570684
## Hospital.CountyMadison                                        -0.1127627
## Hospital.CountyManhattan                                      -0.0729815
## Hospital.CountyMonroe                                          0.4248401
## Hospital.CountyMontgomery                                     -0.1880599
## Hospital.CountyNassau                                          0.0412444
## Hospital.CountyNiagara                                        -0.4589936
## Hospital.CountyOneida                                          0.1211710
## Hospital.CountyOnondaga                                        0.1795457
## Hospital.CountyOntario                                         0.2674217
## Hospital.CountyOrange                                         -0.1827263
## Hospital.CountyOrleans                                        -0.1872032
## Hospital.CountyOswego                                          0.0378860
## Hospital.CountyOtsego                                         -0.0708645
## Hospital.CountyPutnam                                         -0.4084571
## Hospital.CountyQueens                                          0.0132102
## Hospital.CountyRensselaer                                     -0.0345036
## Hospital.CountyRichmond                                               NA
## Hospital.CountyRockland                                       -0.0939019
## Hospital.CountySaratoga                                        0.0222776
## Hospital.CountySchenectady                                    -0.0679061
## Hospital.CountySchuyler                                        0.4324411
## Hospital.CountySt Lawrence                                     0.0073140
## Hospital.CountySteuben                                         0.0133972
## Hospital.CountySuffolk                                                NA
## Hospital.CountySullivan                                       -0.1928288
## Hospital.CountyTompkins                                               NA
## Hospital.CountyUlster                                         -0.1092904
## Hospital.CountyWarren                                         -0.0708293
## Hospital.CountyWayne                                           0.1376048
## Hospital.CountyWestchester                                            NA
## Hospital.CountyWyoming                                                NA
## Hospital.CountyYates                                                  NA
##                                                               Std. Error
## (Intercept)                                                    0.1258292
## Age.Group18 to 29                                              0.0349565
## Age.Group30 to 49                                              0.0346689
## Age.Group50 to 69                                              0.0346190
## Age.Group70 or Older                                           0.0346196
## GenderM                                                        0.0009856
## GenderU                                                        0.7071186
## RaceMulti-racial                                               0.0054169
## RaceOther Race                                                 0.0018322
## RaceWhite                                                      0.0014351
## EthnicityNot Span/Hispanic                                     0.0104056
## EthnicitySpanish/Hispanic                                      0.0105417
## EthnicityUnknown                                               0.0107244
## Type.of.AdmissionEmergency                                     0.0022921
## Type.of.AdmissionNot Available                                 0.0214197
## Type.of.AdmissionTrauma                                        0.0102718
## Type.of.AdmissionUrgent                                        0.0023825
## APR.MDC.Code2                                                  0.0163307
## APR.MDC.Code3                                                  0.0056649
## APR.MDC.Code4                                                  0.0022750
## APR.MDC.Code5                                                  0.0021249
## APR.MDC.Code6                                                  0.0023771
## APR.MDC.Code7                                                  0.0034858
## APR.MDC.Code8                                                  0.0024334
## APR.MDC.Code9                                                  0.0035936
## APR.MDC.Code10                                                 0.0035903
## APR.MDC.Code11                                                 0.0026115
## APR.MDC.Code12                                                 0.0084623
## APR.MDC.Code13                                                 0.0076654
## APR.MDC.Code16                                                 0.0046056
## APR.MDC.Code17                                                 0.0044971
## APR.MDC.Code18                                                 0.0022854
## APR.MDC.Code19                                                 0.0026791
## APR.MDC.Code20                                                 0.0048427
## APR.MDC.Code21                                                 0.0056109
## APR.MDC.Code22                                                 0.0185804
## APR.MDC.Code23                                                 0.0030498
## APR.MDC.Code24                                                 0.0092524
## APR.MDC.Code25                                                 0.0105585
## APR.Severity.of.Illness.Code2                                  0.0019912
## APR.Severity.of.Illness.Code3                                  0.0023041
## APR.Severity.of.Illness.Code4                                  0.0028167
## APR.Risk.of.MortalityMajor                                     0.0018646
## APR.Risk.of.MortalityMinor                                     0.0026987
## APR.Risk.of.MortalityModerate                                  0.0022383
## Ownership.TypeMunicipality                                     0.1204452
## Ownership.TypeNot for Profit Corporation                       0.1204228
## Ownership.TypePublic Benefit Corporation                       0.1204752
## Ownership.TypeState                                            0.1204572
## Facility.TypePrimary Care Hospital - Critical Access Hospital  0.0179634
## Emergency.Department.IndicatorY                                0.0018928
## Health.Service.AreaCentral NY                                  0.0099324
## Health.Service.AreaFinger Lakes                                0.0342516
## Health.Service.AreaHudson Valley                               0.0035078
## Health.Service.AreaLong Island                                 0.0033627
## Health.Service.AreaNew York City                               0.0040771
## Health.Service.AreaSouthern Tier                               0.0205314
## Health.Service.AreaWestern NY                                  0.1215068
## Hospital.CountyAllegany                                        0.1227225
## Hospital.CountyBronx                                           0.0036041
## Hospital.CountyBroome                                          0.0207915
## Hospital.CountyCattaraugus                                     0.1218789
## Hospital.CountyCayuga                                          0.0138656
## Hospital.CountyChautauqua                                      0.1216989
## Hospital.CountyChemung                                         0.0346112
## Hospital.CountyChenango                                               NA
## Hospital.CountyClinton                                         0.0076104
## Hospital.CountyColumbia                                        0.0089202
## Hospital.CountyCortland                                        0.0155548
## Hospital.CountyDelaware                                        0.0352852
## Hospital.CountyDutchess                                        0.0045095
## Hospital.CountyErie                                            0.1214956
## Hospital.CountyEssex                                           0.0411813
## Hospital.CountyFranklin                                        0.0118486
## Hospital.CountyFulton                                          0.0156245
## Hospital.CountyGenesee                                         0.1221492
## Hospital.CountyHerkimer                                        0.0308655
## Hospital.CountyJefferson                                       0.0124533
## Hospital.CountyKings                                           0.0034264
## Hospital.CountyLewis                                           0.1258666
## Hospital.CountyLivingston                                      0.0382218
## Hospital.CountyMadison                                         0.0170772
## Hospital.CountyManhattan                                       0.0033067
## Hospital.CountyMonroe                                          0.0342049
## Hospital.CountyMontgomery                                      0.0087912
## Hospital.CountyNassau                                          0.0025210
## Hospital.CountyNiagara                                         0.1215929
## Hospital.CountyOneida                                          0.0103898
## Hospital.CountyOnondaga                                        0.0099498
## Hospital.CountyOntario                                         0.0347781
## Hospital.CountyOrange                                          0.0042624
## Hospital.CountyOrleans                                         0.1241328
## Hospital.CountyOswego                                          0.0141012
## Hospital.CountyOtsego                                          0.0067461
## Hospital.CountyPutnam                                          0.0093391
## Hospital.CountyQueens                                          0.0035270
## Hospital.CountyRensselaer                                      0.0067658
## Hospital.CountyRichmond                                               NA
## Hospital.CountyRockland                                        0.0046061
## Hospital.CountySaratoga                                        0.0074194
## Hospital.CountySchenectady                                     0.0053394
## Hospital.CountySchuyler                                        0.0405075
## Hospital.CountySt Lawrence                                     0.0123773
## Hospital.CountySteuben                                         0.0356921
## Hospital.CountySuffolk                                                NA
## Hospital.CountySullivan                                        0.0113428
## Hospital.CountyTompkins                                               NA
## Hospital.CountyUlster                                          0.0065610
## Hospital.CountyWarren                                          0.0062599
## Hospital.CountyWayne                                           0.0357522
## Hospital.CountyWestchester                                            NA
## Hospital.CountyWyoming                                                NA
## Hospital.CountyYates                                                  NA
##                                                                z value Pr(>|z|)
## (Intercept)                                                      5.286 1.25e-07
## Age.Group18 to 29                                               17.504  < 2e-16
## Age.Group30 to 49                                               16.561  < 2e-16
## Age.Group50 to 69                                               16.236  < 2e-16
## Age.Group70 or Older                                            14.109  < 2e-16
## GenderM                                                         -8.977  < 2e-16
## GenderU                                                         -0.440 0.660106
## RaceMulti-racial                                                -1.703 0.088590
## RaceOther Race                                                 -41.703  < 2e-16
## RaceWhite                                                      -40.515  < 2e-16
## EthnicityNot Span/Hispanic                                       4.888 1.02e-06
## EthnicitySpanish/Hispanic                                       -0.227 0.820351
## EthnicityUnknown                                                 4.382 1.18e-05
## Type.of.AdmissionEmergency                                     -43.797  < 2e-16
## Type.of.AdmissionNot Available                                  -7.311 2.65e-13
## Type.of.AdmissionTrauma                                          2.828 0.004681
## Type.of.AdmissionUrgent                                         36.249  < 2e-16
## APR.MDC.Code2                                                   -9.474  < 2e-16
## APR.MDC.Code3                                                  -31.443  < 2e-16
## APR.MDC.Code4                                                  -40.837  < 2e-16
## APR.MDC.Code5                                                  -85.896  < 2e-16
## APR.MDC.Code6                                                   -5.536 3.09e-08
## APR.MDC.Code7                                                  -13.018  < 2e-16
## APR.MDC.Code8                                                    0.985 0.324581
## APR.MDC.Code9                                                    4.133 3.58e-05
## APR.MDC.Code10                                                 -63.049  < 2e-16
## APR.MDC.Code11                                                 -55.794  < 2e-16
## APR.MDC.Code12                                                 -24.402  < 2e-16
## APR.MDC.Code13                                                 -18.002  < 2e-16
## APR.MDC.Code16                                                 -25.088  < 2e-16
## APR.MDC.Code17                                                  49.868  < 2e-16
## APR.MDC.Code18                                                 -32.895  < 2e-16
## APR.MDC.Code19                                                 416.609  < 2e-16
## APR.MDC.Code20                                                  71.585  < 2e-16
## APR.MDC.Code21                                                 -41.316  < 2e-16
## APR.MDC.Code22                                                  27.801  < 2e-16
## APR.MDC.Code23                                                 167.649  < 2e-16
## APR.MDC.Code24                                                 -11.342  < 2e-16
## APR.MDC.Code25                                                   8.173 3.01e-16
## APR.Severity.of.Illness.Code2                                  135.688  < 2e-16
## APR.Severity.of.Illness.Code3                                  267.193  < 2e-16
## APR.Severity.of.Illness.Code4                                  405.432  < 2e-16
## APR.Risk.of.MortalityMajor                                     -83.845  < 2e-16
## APR.Risk.of.MortalityMinor                                    -182.848  < 2e-16
## APR.Risk.of.MortalityModerate                                 -153.390  < 2e-16
## Ownership.TypeMunicipality                                       6.255 3.98e-10
## Ownership.TypeNot for Profit Corporation                         4.702 2.58e-06
## Ownership.TypePublic Benefit Corporation                         6.970 3.17e-12
## Ownership.TypeState                                              5.104 3.33e-07
## Facility.TypePrimary Care Hospital - Critical Access Hospital  -12.140  < 2e-16
## Emergency.Department.IndicatorY                                -20.535  < 2e-16
## Health.Service.AreaCentral NY                                  -20.813  < 2e-16
## Health.Service.AreaFinger Lakes                                -11.768  < 2e-16
## Health.Service.AreaHudson Valley                                18.095  < 2e-16
## Health.Service.AreaLong Island                                   4.185 2.85e-05
## Health.Service.AreaNew York City                                15.444  < 2e-16
## Health.Service.AreaSouthern Tier                               -13.761  < 2e-16
## Health.Service.AreaWestern NY                                    3.509 0.000450
## Hospital.CountyAllegany                                         -5.195 2.05e-07
## Hospital.CountyBronx                                             3.485 0.000493
## Hospital.CountyBroome                                            7.447 9.53e-14
## Hospital.CountyCattaraugus                                      -5.907 3.49e-09
## Hospital.CountyCayuga                                           -4.279 1.88e-05
## Hospital.CountyChautauqua                                       -5.213 1.86e-07
## Hospital.CountyChemung                                           8.063 7.44e-16
## Hospital.CountyChenango                                             NA       NA
## Hospital.CountyClinton                                          -0.169 0.866166
## Hospital.CountyColumbia                                          3.302 0.000961
## Hospital.CountyCortland                                         -6.931 4.17e-12
## Hospital.CountyDelaware                                         -1.196 0.231789
## Hospital.CountyDutchess                                        -53.497  < 2e-16
## Hospital.CountyErie                                             -4.564 5.02e-06
## Hospital.CountyEssex                                            -3.547 0.000389
## Hospital.CountyFranklin                                        -26.195  < 2e-16
## Hospital.CountyFulton                                          -18.724  < 2e-16
## Hospital.CountyGenesee                                          -5.956 2.58e-09
## Hospital.CountyHerkimer                                          5.954 2.61e-09
## Hospital.CountyJefferson                                        16.102  < 2e-16
## Hospital.CountyKings                                            -6.253 4.03e-10
## Hospital.CountyLewis                                             4.141 3.46e-05
## Hospital.CountyLivingston                                        9.342  < 2e-16
## Hospital.CountyMadison                                          -6.603 4.03e-11
## Hospital.CountyManhattan                                       -22.071  < 2e-16
## Hospital.CountyMonroe                                           12.420  < 2e-16
## Hospital.CountyMontgomery                                      -21.392  < 2e-16
## Hospital.CountyNassau                                           16.361  < 2e-16
## Hospital.CountyNiagara                                          -3.775 0.000160
## Hospital.CountyOneida                                           11.662  < 2e-16
## Hospital.CountyOnondaga                                         18.045  < 2e-16
## Hospital.CountyOntario                                           7.689 1.48e-14
## Hospital.CountyOrange                                          -42.869  < 2e-16
## Hospital.CountyOrleans                                          -1.508 0.131532
## Hospital.CountyOswego                                            2.687 0.007216
## Hospital.CountyOtsego                                          -10.504  < 2e-16
## Hospital.CountyPutnam                                          -43.736  < 2e-16
## Hospital.CountyQueens                                            3.745 0.000180
## Hospital.CountyRensselaer                                       -5.100 3.40e-07
## Hospital.CountyRichmond                                             NA       NA
## Hospital.CountyRockland                                        -20.386  < 2e-16
## Hospital.CountySaratoga                                          3.003 0.002677
## Hospital.CountySchenectady                                     -12.718  < 2e-16
## Hospital.CountySchuyler                                         10.676  < 2e-16
## Hospital.CountySt Lawrence                                       0.591 0.554573
## Hospital.CountySteuben                                           0.375 0.707397
## Hospital.CountySuffolk                                              NA       NA
## Hospital.CountySullivan                                        -17.000  < 2e-16
## Hospital.CountyTompkins                                             NA       NA
## Hospital.CountyUlster                                          -16.658  < 2e-16
## Hospital.CountyWarren                                          -11.315  < 2e-16
## Hospital.CountyWayne                                             3.849 0.000119
## Hospital.CountyWestchester                                          NA       NA
## Hospital.CountyWyoming                                              NA       NA
## Hospital.CountyYates                                                NA       NA
##                                                                  
## (Intercept)                                                   ***
## Age.Group18 to 29                                             ***
## Age.Group30 to 49                                             ***
## Age.Group50 to 69                                             ***
## Age.Group70 or Older                                          ***
## GenderM                                                       ***
## GenderU                                                          
## RaceMulti-racial                                              .  
## RaceOther Race                                                ***
## RaceWhite                                                     ***
## EthnicityNot Span/Hispanic                                    ***
## EthnicitySpanish/Hispanic                                        
## EthnicityUnknown                                              ***
## Type.of.AdmissionEmergency                                    ***
## Type.of.AdmissionNot Available                                ***
## Type.of.AdmissionTrauma                                       ** 
## Type.of.AdmissionUrgent                                       ***
## APR.MDC.Code2                                                 ***
## APR.MDC.Code3                                                 ***
## APR.MDC.Code4                                                 ***
## APR.MDC.Code5                                                 ***
## APR.MDC.Code6                                                 ***
## APR.MDC.Code7                                                 ***
## APR.MDC.Code8                                                    
## APR.MDC.Code9                                                 ***
## APR.MDC.Code10                                                ***
## APR.MDC.Code11                                                ***
## APR.MDC.Code12                                                ***
## APR.MDC.Code13                                                ***
## APR.MDC.Code16                                                ***
## APR.MDC.Code17                                                ***
## APR.MDC.Code18                                                ***
## APR.MDC.Code19                                                ***
## APR.MDC.Code20                                                ***
## APR.MDC.Code21                                                ***
## APR.MDC.Code22                                                ***
## APR.MDC.Code23                                                ***
## APR.MDC.Code24                                                ***
## APR.MDC.Code25                                                ***
## APR.Severity.of.Illness.Code2                                 ***
## APR.Severity.of.Illness.Code3                                 ***
## APR.Severity.of.Illness.Code4                                 ***
## APR.Risk.of.MortalityMajor                                    ***
## APR.Risk.of.MortalityMinor                                    ***
## APR.Risk.of.MortalityModerate                                 ***
## Ownership.TypeMunicipality                                    ***
## Ownership.TypeNot for Profit Corporation                      ***
## Ownership.TypePublic Benefit Corporation                      ***
## Ownership.TypeState                                           ***
## Facility.TypePrimary Care Hospital - Critical Access Hospital ***
## Emergency.Department.IndicatorY                               ***
## Health.Service.AreaCentral NY                                 ***
## Health.Service.AreaFinger Lakes                               ***
## Health.Service.AreaHudson Valley                              ***
## Health.Service.AreaLong Island                                ***
## Health.Service.AreaNew York City                              ***
## Health.Service.AreaSouthern Tier                              ***
## Health.Service.AreaWestern NY                                 ***
## Hospital.CountyAllegany                                       ***
## Hospital.CountyBronx                                          ***
## Hospital.CountyBroome                                         ***
## Hospital.CountyCattaraugus                                    ***
## Hospital.CountyCayuga                                         ***
## Hospital.CountyChautauqua                                     ***
## Hospital.CountyChemung                                        ***
## Hospital.CountyChenango                                          
## Hospital.CountyClinton                                           
## Hospital.CountyColumbia                                       ***
## Hospital.CountyCortland                                       ***
## Hospital.CountyDelaware                                          
## Hospital.CountyDutchess                                       ***
## Hospital.CountyErie                                           ***
## Hospital.CountyEssex                                          ***
## Hospital.CountyFranklin                                       ***
## Hospital.CountyFulton                                         ***
## Hospital.CountyGenesee                                        ***
## Hospital.CountyHerkimer                                       ***
## Hospital.CountyJefferson                                      ***
## Hospital.CountyKings                                          ***
## Hospital.CountyLewis                                          ***
## Hospital.CountyLivingston                                     ***
## Hospital.CountyMadison                                        ***
## Hospital.CountyManhattan                                      ***
## Hospital.CountyMonroe                                         ***
## Hospital.CountyMontgomery                                     ***
## Hospital.CountyNassau                                         ***
## Hospital.CountyNiagara                                        ***
## Hospital.CountyOneida                                         ***
## Hospital.CountyOnondaga                                       ***
## Hospital.CountyOntario                                        ***
## Hospital.CountyOrange                                         ***
## Hospital.CountyOrleans                                           
## Hospital.CountyOswego                                         ** 
## Hospital.CountyOtsego                                         ***
## Hospital.CountyPutnam                                         ***
## Hospital.CountyQueens                                         ***
## Hospital.CountyRensselaer                                     ***
## Hospital.CountyRichmond                                          
## Hospital.CountyRockland                                       ***
## Hospital.CountySaratoga                                       ** 
## Hospital.CountySchenectady                                    ***
## Hospital.CountySchuyler                                       ***
## Hospital.CountySt Lawrence                                       
## Hospital.CountySteuben                                           
## Hospital.CountySuffolk                                           
## Hospital.CountySullivan                                       ***
## Hospital.CountyTompkins                                          
## Hospital.CountyUlster                                         ***
## Hospital.CountyWarren                                         ***
## Hospital.CountyWayne                                          ***
## Hospital.CountyWestchester                                       
## Hospital.CountyWyoming                                           
## Hospital.CountyYates                                             
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for poisson family taken to be 1)
## 
##     Null deviance: 3769874  on 646523  degrees of freedom
## Residual deviance: 2548733  on 646418  degrees of freedom
##   (4282 observations deleted due to missingness)
## AIC: 4725404
## 
## Number of Fisher Scoring iterations: 5

# Evaluate Poisson model
eval_LOS_Poi <- evaluate_model(Poi, test, "Length.of.Stay")

## Error in model.frame.default(Terms, newdata, na.action = na.action, xlev = object$xlevels): factor Hospital.County has new levels Schoharie

Note, the same hospital county coefficients were not estimated in using the Poisson model either.

6.2.3 Zero-Truncated Poisson Model

Next we look at the Zero-Truncated Poisson model. This is a modification of the Poisson model, and it can only take integer values from 1 to infinity. Therfore, this model is more appropriate to model length of stay because it will never take 0 values.

# GLM with zero-truncated Poisson
ZeroTruncated_Poi <- glm(Length.of.Stay ~ Age.Group + Gender + Race + Ethnicity + 
    Type.of.Admission + APR.MDC.Code + APR.Severity.of.Illness.Code + APR.Risk.of.Mortality + 
    Ownership.Type + Facility.Type + Emergency.Department.Indicator + Health.Service.Area + 
    Hospital.County, family = Tpoisson(link = "log"), data = train)
summary(ZeroTruncated_Poi)

# Evaluate Zero-Truncated Poisson model
eval_LOS_ZeroTruncPoi <- evaluate_model(ZeroTruncated_Poi, test, "Length.of.Stay")

6.2.4 Hierarchical Zero-Truncated Poisson Model

Lastly, we fit a hierarchical zero-truncted poisson model. If you look at the variables for Health Serivce Area and Hospital County, you can see that these are nested varaibles. For example, specific hospital counties will only occur in specific health areas. By modeling length of stay as a multi-level model, we can take into account the area-level and county-level effects on length of stay by accounting for unexplained variation in hospital service areas and hospital counties.

# GLM with zero-truncated Poisson, nesting
Hierarchical_LOS <- HLfit(Length.of.Stay ~ Age.Group + Gender + Race + Ethnicity + 
    Type.of.Admission + APR.MDC.Code + APR.Severity.of.Illness.Code + APR.Risk.of.Mortality + 
    Ownership.Type + Facility.Type + Emergency.Department.Indicator + (1 | Hospital.County/Health.Service.Area), 
    family = Tpoisson(link = "log"), data = train)
summary(Hierarchical_LOS, details = TRUE, max.print = 99999999)

# Evaluate Hierarchical LOS model
eval_LOS_Hier <- evaluate_model(Hierarchical_LOS, test, "Length.of.Stay")

6.2.5 Model Comparison

# compare <- data.frame(matrix(, nrow = 3, ncol = 5)) colnames(compare) <- c('',
# 'Linear Regression', 'Poisson', 'Zero-Truncated Poisson','Hierarchical
# Zero-Truncated Poisson')

# #Factor compare[1,1] <- 'Mean Absolute Error' compare[2,1] <- 'Mean Relative
# Error' compare[3,1] <- 'Root Mean Squared Error'


LOS_compare <- cbind(`Linear Regression` = eval_LOS_linear, `Poisson Model` = eval_LOS_Poi, 
    `ZTPoisson Model` = eval_LOS_ZeroTruncPoi, `Hierarchical ZTPoisson` = eval_LOS_Hier)

# #Linear Regression compare[1,2] <- eval_LOS_linear[1] compare[2,2] <-
# eval_LOS_linear[2] compare[3,2] <- eval_LOS_linear[3]

# # Poisson compare[1,3] <- eval_LOS_Poi[1] compare[2,3] <- eval_LOS_Poi[2]
# compare[3,3] <- eval_LOS_Poi[3]

# # Zero-Truncated Poisson compare[1,4] <- eval_LOS_ZeroTruncPoi[1] compare[2,4]
# <- eval_LOS_ZeroTruncPoi[2] compare[3,4] <- eval_LOS_ZeroTruncPoi[3]

# # Hierarchical Zero Truncated Poisson compare[1,5] <- eval_LOS_Hier[1]
# compare[2,5] <- eval_LOS_Hier[2] compare[3,5] <- eval_LOS_Hier[3]


# Print table
report_table(LOS_compare, rownames = TRUE)

6.3 Cost per Day

6.3.1 Linear Regression

In predicting cost per day, we focused on comparing simple linear regression results to the results for a hierarchical linear model accounting for the variance in serivce area and hospital county. We predicted that we would see an improvement in performance by using a more complicated and computationally heavy approach using the hierarchical structure since it would account for the structure of the data.

# Linear regression for cost per day
linearReg_Cost <- lm(Cost.per.Day ~ Age.Group + Gender + Race + Ethnicity + Type.of.Admission + 
    APR.MDC.Code + APR.Severity.of.Illness.Code + APR.Risk.of.Mortality + Ownership.Type + 
    Facility.Type + Emergency.Department.Indicator + Health.Service.Area + Hospital.County, 
    data = train)
summary(linearReg_Cost)

R_squared2 = round(summary(linearReg_Cost)$r.squared, 4)

# Evaluate Linear regression cost per day model
eval_Cost_linear <- evaluate_model(linearReg_Cost, test, "Cost.per.Day")

7 coefficients were not estimated due to singularities similarly to the results from the length of stay analysis.

6.3.2 Hierarchical Linear Regression

Hierarchical_cost <- lmer(Cost.per.Day ~ Age.Group + Gender + Race + Ethnicity + 
    Type.of.Admission + APR.MDC.Code + APR.Severity.of.Illness.Code + APR.Risk.of.Mortality + 
    Ownership.Type + Facility.Type + Emergency.Department.Indicator + (1 | Hospital.County/Health.Service.Area), 
    data = train)

summary(Hierarchical_cost)

# Evaluation Hierarchical model for cost per day
eval_Cost_Hier <- evaluate_model(Hierarchical_cost, test, "Cost.per.Day")

6.3.3 Model Comparison

# compare2 <- data.frame(matrix(, nrow = 3, ncol = 3)) colnames(compare2) <-
# c('', 'Linear Regression', 'Hierarchical Linear Regression')


# #Factor compare2[1,1] <- 'Mean Absolute Error' compare2[2,1] <- 'Mean Relative
# Error' compare2[3,1] <- 'Root Mean Squared Error'

# #Linear Regression compare2[1,2] <- eval_Cost_linear[1] compare2[2,2] <-
# eval_Cost_linear[2] compare2[3,2] <- eval_Cost_linear[3]

# # Hierarchical Linear Regression compare2[1,3] <- eval_Cost_Hier[1]
# compare2[2,3] <- eval_Cost_Hier[2] compare2[3,3] <- eval_Cost_Hier[3]

CPD_compare = cbind(`Linear Regression` = eval_Cost_linear, `Hierarchical Linear Regression` = eval_Cost_Hier)

# Print table
report_table(CPD_compare, rownames = TRUE)

7 Discussion

We did not see a large increase in predictive power as we expected by using the hierarchical linear model in either of the two predictions. The evaluation metrics between the two methods are very similar indicating that there wasn’t much to gain in performance by using the more computationally intensive method.However, the reward you do get for running the hierarchical model is that it better represents the structure of the data, and it knows how to treat the nested variables. Since linear regression does not have the knowledge of the correlation between the nested variables, it ends up not being able to estimate certain coefficients and you get the warning “prediction from a rank-deficient fit may be misleading” when trying to predict using the linear regression model. Thus, it is better to take into account the hierarchical structure of the results to be able to trust the results of your predictions.

If we wanted to use a model to predict length of stay, in practice we don’t want the model to predict -1.5 because that would not be a realistic prediction. At least, by using a zero-truncated poisson for predicting length of stay, we are taking into account that the predicted value should be at least 1.

For the cost per day analysis, we believe we may not have seen much of a difference between the two techniques because there is likely not much difference in cost between hospitals, especially between hospitals in the same general area.

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